DBA QUESTION #3
How is the distributive property used when finding the product of two polynomials?
Give an example.
How are polynomials closed under multiplication?

Answer:$168 per hour

Step-by-step explanation: so in a half hour they charge $84 .

a half hour is 30 minutes and you need another half hour so double $84

$84x2=168

we can use the fact that anything multiplied by 1 results in the same value to simplify the expression:

   (3x + 2)(x - 5) / (3x + 4)(x - 5)  =  (3x + 2)/(3x + 4)

To obtain an equivalent expression for (3x+2)/(x-5) with a denominator of (3x+4)(x-5), we can use the distributive property to expand the numerator and denominator:

   (3x + 2) / (x - 5)  =  (3x + 2)(x - 5) / (3x + 4)(x - 5)

From here, we can use the fact that anything multiplied by 1 results in the same value to simplify the expression:

   (3x + 2)(x - 5) / (3x + 4)(x - 5)  =  (3x + 2)/(3x + 4)

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According to the model, the expected salary for a CEO of a firm with $5,000,000 in sales and $20,000,000 in market value is $2,178,357 or between $1,139,522 and $4,056,537.  Therefore, asking for $500,000 as an annual salary would be significantly lower than what the model predicts.

According to the model from part (a), the equation for the logarithm of annual salary is:

log(salary) = 4.62 + 0.16 sales + 0.11 log(mktval) + u

where u is the error term. This model has a multiple R-squared of 0.30, which means that it explains 30% of the variation in salaries based on sales and market value.

log(salary) = 4.62 + 0.16 x log(500000) + 0.11 x log(20000000)

log(salary) = 4.62 + 0.16 x 13.122 + 0.11 x 16.811

log(salary) = 7.625

salary = exp(7.625)

salary = $2,178,357

We can also use the coefficients from the model to calculate the expected salary directly, without taking logarithms.

salary = exp(β0) x sales^β1 x mktval^β2 x e^u

salary = exp(4.62) x 5,000,000^0.16 x 20,000,000^0.11 x e^u

salary = $2,178,357 x e^u

Using this assumption, we can calculate a 95% confidence interval for the expected salary:

log(salary) = 7.625

standard error = 535.9 x sqrt(0.16^2 + 0.11^2) = 136.6

95% confidence interval = exp(log(salary) ± 1.96 x standard error)

95% confidence interval = $1,139,522 to $4,056,537

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The simplified rational expression is (x³-6x²+5x²)-30x+5x²-30x+25x-150)/(x³+17x²+75x+175)

To simplify the rational expression, we will need to use multiplication and division of the rational expressions. We will also need to factor the expressions in order to simplify them.

First, let's factor the expressions:
(x²-3x-18)/(x²+10x+21)-:(x²+3x-54)/(x²-x-30)*(x²+16x+63)/(x²+14x+45)

= ((x-6)(x+3))/((x+7)(x+3))-:((x+9)(x-6))/((x-6)(x+5))*((x+9)(x+7))/((x+9)(x+5))

Next, let's simplify the expressions by canceling out the common factors:
= (x-6)/(x+7)-: (x+9)/(x+5)*(x+7)/(x+5)
= (x-6)/(x+7)-: (x+9)(x+7)/(x+5)(x+5)

Now, let's multiply the expressions:
= (x-6)(x+5)(x+5)/(x+7)(x+5)(x+5) - (x+9)(x+7)(x+7)/(x+7)(x+5)(x+5)

Finally, let's subtract the expressions:
= ((x-6)(x+5)(x+5) - (x+9)(x+7)(x+7))/((x+7)(x+5)(x+5))
= (x³-6x²+5x²-30x+5x²-30x+25x-150)/(x²+17x²+75x+175)

Therefore, the simplified rational expression is:
= (x³-6x²+5x²-30x+5x²-30x+25x-150)/(x³+17x²+75x+175)

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M' A'T" H' is (1,1) and (2.5) equals 3.6 to form a quadrilateral. A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.

Let the scale factor of quadrilateral is center at 2.5 at (1, 1) then

(1,1) and (2.5) equals 3.6

(1,1) + (2.5) =  3.6

Therefore, the statement exists true about the dilation is

D. [tex]\frac{}{A'T'}[/tex] will overlap [tex]\frac{}{AT}[/tex]

A. [tex]\frac{}{M'A'}[/tex] will overlap [tex]\frac{}{MA}[/tex]

E. The slope of [tex]\frac{}{HT}[/tex] is equal to the slope of [tex]\frac{}{H'T'}[/tex]

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The equation of the midline of the sinusoidal function will be y = 4.

The most obvious representation of the amount that objects, in reality, modify their state is a sinusoidal waveform or sinusoidal wave. A sine wave depicts how the intensity of a variable varies over time. For example, the variable may be an audible sound.

The sinusoidal equation is written as,

y = A sin (ωt + ∅) + k

Here, 'A' is the amplitude, 'ω' is the frequency, and '∅' is the phase difference.

From the graph, it can be seen that the function is shifted upward by four units. Then the equation of the midline of the sine function is given as,

y = 4

The equation of the midline of the sinusoidal function will be y = 4.

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For Part 1 of 2 (a): The exact distance between the points (2,73) and (-22,3) is 74.
For Part 2 of 2 (b): The midpoint of the line segment whose endpoints are the given points is (−10,38).

(a) The exact distance between the points is found using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

Where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in the values from the given points:

d = √[(-22 - 2)² + (3 - 73)²]

Simplifying:

d = √[(-24)² + (-70)²]

d = √[576 + 4900]

d = √[5476]

d = 74

Therefore, the exact distance between the points is 74.


(b) The midpoint of the line segment whose endpoints are the given points is found using the midpoint formula:

M = [(x1 + x2)/2, (y1 + y2)/2]

Where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in the values from the given points:

M = [(2 + (-22))/2, (73 + 3)/2]

Simplifying:

M = [(-20)/2, (76)/2]

M = [-10, 38]

Therefore, the midpoint is (-10, 38).

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Var(θ3) = (a-1)(a-2) / λ^2 - θ^2.

First, let's find the method of moments estimate of θ based on Y1,...,Yn. We know that E(Y) = E(log(X/x0)) = E(log(X)) - log(x0) = θ^-1 - log(x0). Therefore, θ^-1 = E(Y) + log(x0) and θ3 = 1 / (E(Y) + log(x0)).

Next, let's find the distribution of Y. Since Y = log(X/x0), we can use the change of variables formula to find the density function of Y. Let g(y) = x0 * exp(y), then the Jacobian is |g'(y)| = x0 * exp(y). The density function of Y is fY(y) = fX(g(y)) * |g'(y)| = θ * (x0 * exp(y))^θ * (x0 * exp(y))^(-θ-1) * x0 * exp(y) = θ * x0^θ * exp(-θy).

Finally, let's find the mean and variance of θ3. We know that E(θ3) = E(1 / (E(Y) + log(x0))) = 1 / (E(Y) + log(x0)) = θ. To find the variance, we can use the fact that Var(θ3) = E(θ3^2) - E(θ3)^2. We can use the fact that if U follows a gamma distribution, then E(U^r) = Γ(a+r) / [λ^r * Γ(a)] to find E(θ3^2). Let U = E(Y) + log(x0), then E(θ3^2) = E(U^-2) = Γ(a-2) / [λ^2 * Γ(a)] = (a-1)(a-2) / λ^2. Therefore, Var(θ3) = (a-1)(a-2) / λ^2 - θ^2.

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Answer:

Let's first simplify the left-hand side and right-hand side of the inequality:

2 - 5(x + 1) = 2 - 5x - 5 = -5x - 3 3(x - 1) - 24 = 3x - 27

So the inequality becomes:

-5x - 3 ≥ 3x - 27

Now we can solve for x:

-5x - 3 ≥ 3x - 27 -8x ≥ -24 x ≤ 3

The solution set is all x-values less than or equal to 3. We can express this in interval notation as:

(-∞, 3]

The solution set in interval notation is (-∞, 4].

To solve the inequality 2 − 5(x + 1) ≥ 3(x − 1) − 24 and write the solution set in interval notation, we need to follow these steps:

Distribute the -5 and 3 on the left and right sides of the inequality, respectively:
2 - 5x - 5 ≥ 3x - 3 - 24

Simplify both sides of the inequality by combining like terms:
-3x - 3 ≥ 3x - 27

Add 3x to both sides of the inequality to isolate the variable on one side:
-3 ≥ 6x - 27

Add 27 to both sides of the inequality:
24 ≥ 6x

Divide both sides of the inequality by 6 to solve for x:
4 ≥ x

Write the solution set in interval notation. Since the inequality is "greater than or equal to," we use a closed bracket for the lower bound and an open bracket for the upper bound:
(-∞, 4]

Therefore, the solution set in interval notation is (-∞, 4].

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In the following question, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

To find the surface area of the scratching post, we need to add up the surface areas of all the sides.

The scratching post has a rectangular prism shape with dimensions of 10 cm x 10 cm x 90 cm. The bottom is also a 10 cm x 10 cm square.

So the surface area of the post, including the bottom, is:

2(10 cm x 10 cm) + 2(10 cm x 90 cm) + 2(10 cm x 10 cm) = 200 cm^2 + 1800 cm^2 + 200 cm^2 = 2200 cm^2

Therefore, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

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As a financial analyst, I should opt for an Initial cost of $125000 and after all the making and labor charges each bike is made under $225.

When a linear function is exposed to various constraints, it is maximized or reduced using the mathematical modeling technique known as linear programming. In corporate planning, industrial engineering, and other fields, this technique has proven helpful for guiding quantitative judgments.

Given, The Bici bicycle company is making a low-price ultra-light bicycle.

They have two plans,

I. Initial cost of $125000 and after all the making and labor charges

each bike is made under $225.

II. Initial cost of $100000 and after all the making and labor charges

each bike is made for under $275.

As they want bicycles to cost less we should opt for the first plan even if the initial cost is more, As the market demand is for a cycle that is low in price so it would sell more and an extra investment of $25000 won't be wasted.

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Answer:

The correct answer is 4th degree polynomial.

The other vertices appears to be located in the second and fourth quadrants.

What is a polygon?

A polygon is a two-dimensional geometric shape that is made up of straight line segments connected end-to-end to form a closed shape.

Based on the image, it appears that we are dealing with a polygon JKLMNO on a coordinate grid.

First, we can see that the polygon is a hexagon (six-sided figure) with vertices at points J, K, L, M, N, and O. We can also see that the polygon is not a regular hexagon, since its sides are of different lengths and its angles are not all equal.

To determine the coordinates of the vertices of the polygon, we would need to know the scale and orientation of the coordinate grid. However, based on the image, we can make some general observations about the location of the vertices. For example, we can see that vertex J appears to be in the third quadrant (negative x and y values), while vertex N appears to be in the first quadrant (positive x and y values).

Therefore,  The other vertices appear to be located in the second and fourth quadrants.

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Answer:

x = 60

Step-by-step explanation: The sum of the exterior angles of any polygon is always equal to 360 degrees, including for a parallelogram. This means that if you add up all the exterior angles of a parallelogram, the total will always be 360 degrees.

hence :

2x + 2x + x + x = 360, for the given figure

=> 6x = 360

dividing by 6 both sides

x = 60

Answer:

x = 25

Step-by-step explanation:

We know

5x - 35 is a right angle, meaning it must be 90 degree.

Let's solve

5x - 35 = 90

5x = 125

x = 25

The polynomial f(x) of degree 3 with real coefficients and the given zeros is f(x) = x³ - x² + 4x + 2.

To find a polynomial f(x) of degree 3 with real coefficients and the given zeros, we need to use the fact that if a polynomial has a complex root, then its conjugate is also a root. This means that if 1-i is a root, then 1+i is also a root.

So, our polynomial f(x) has the following roots: -1, 1-i, 1+i.

We can write the polynomial as the product of its factors:

f(x) = (x - (-1))(x - (1-i))(x - (1+i))

Simplifying the factors:

f(x) = (x + 1)(x - 1 + i)(x - 1 - i)

Multiplying the factors:

f(x) = (x + 1)(x² - 2x + 2)

Expanding the polynomial:

f(x) = x³ - 2x² + 2x + x² - 2x + 2

Simplifying the polynomial:

f(x) = x³ - x² + 4x + 2

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Mateo takes 20 minutes to run around the track once.

The rate at which an object goes from one location to another is known as its speed. It is described as the distance that an object covers in a certain amount of time. The distance traveled in one unit of time is typically used to express speed, such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph) (mph).

[tex]Speed = \frac{distance}{time }[/tex]

Here we assume that the distance around the track is 'd', Adrian's speed is 'a' (in distance per minute) and Mateo's speed is 'm' (also in distance per minute).

Since Adrian takes 15 minutes to run around the track once, we have:

a = d/15

Let's use the formula: time = distance/speed

to write two equations for the total distance traveled by each boy.

For Adrian: 2d = a × 30

For Mateo: 2d = m × t

where 't' is the time it takes Mateo to run around the track once.

Since we know that Mateo runs faster than Adrian, we have:

m > a

Substituting the expression we found for 'a' into the equation for Adrian, we get:

2d = (d/15) × 30

d = 225

Now, we can solve for Mateo's speed using the equation for the total distance traveled by Mateo:

2d = m × t

2(225) = m × t

m = 450/t

Substituting this expression for 'm' into the inequality m > a, we get:

450/t > d/15

15×450 > d×t

6750 > d×t

Substituting d = 225, we get:

6750 > 225t

t < 30

Since Mateo takes less than 30 minutes to run around the track once, and we know that Adrian takes 15 minutes, the possible value for t is 20 minutes: t = 20.

Therefore, Mateo takes 20 minutes to run around the track once.

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The number that if decreased by one fifth of itself gives 132 is 165.

To solve this problem, we can use algebra to create an equation and then solve for the unknown number.

Let x be the number we are trying to find.

If the number decreased by one-fifth of itself yields 132, we can write the equation:

x - (1/5)x = 132

Simplifying the equation, we get:

(4/5)x = 132

Multiplying both sides by 5/4 to isolate x, we get:

x = (5/4)(132)

x = 165

Therefore, the number that decreased by one-fifth of itself yields 132 is 165.

Alternatively, we can use a different method to solve the problem.

If the number decreased by one-fifth of itself yields 132, we can write the equation:

x - (x/5) = 132

Multiplying both sides by 5 to eliminate the fraction, we get:

5x - x = 660

Simplifying the equation, we get:

4x = 660

Dividing both sides by 4 to isolate x, we get:

x = 165

Therefore, the number that decreased by one-fifth of itself yields 132 is 165.

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Answer:

Let's call the number of packs of skimmed milk "S" and the number of packs of full cream milk "F".

We know that the total number of packs of milk is 1350:

F + L + S = 1350

We also know that there are 150 more packs of skimmed milk than low fat milk:

S = L + 150

And we know that there are 465 packs of low fat milk:

L = 465

We can substitute L=465 into the equation S=L+150 to get:

S = 465 + 150 = 615

Now we can use the first equation to solve for F:

F + L + S = 1350

F + 465 + 615 = 1350

F = 270

Therefore, there are 270 packs of full cream milk.

Answer:

Step-by-step explanation:

OK so 54318+21298=75616.

So i divided 75600 by 2 and got 37800 as an answer. So that means that 37800+37800=75600.

The value of RU, considering the Triangle Midsegment Theorem, is given as follows:

RU = 35.

The value of RU is obtained applying the proportions in the context of the problem.

A proportion is applied as the Triangle Midsegment Theorem states that the midsegment of a triangle is parallel to it's base, and has the length half as long.

The length of the base is of ST = 70, hence the length of the midsegement is given as follows:

RU = 0.5ST

RU = 0.5 x 70

RU = 35.

(the length of the midsegment is half the length of the base, hence we apply the proportion multiplying by 0.5).

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Using multiplicative property of equations, the solution to the equation is x = 32.

The multiplicative property of equations states that if you multiply both sides of an equation by the same number, the equation will still be true.

In this case, we can use the multiplicative property to solve for x by multiplying both sides of the equation by (4/3) to cancel out the fraction on the right side of the equation.

24 = (3/4)x

(4/3)(24) = (4/3)(3/4)x

32 = x

So the solution to this equation is x = 32.

No need to further simplify your answer since the solution is already in its simplest form.

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The constraints should also include the fact that the total donated StandardSoap must equal 500L

Q1: You should remove the constraints related to the purchasing limits from your LP, such as the limit of 4000L of lotion, 5000L of soap, and 750L of SpecialX.

Q2: In Excel, your objective function should be to maximize the monthly profit, which can be determined by subtracting the total costs of producing Moisturizing+ and StandardSoap from the total revenue of the hand sanitizer sold on the market and donated to charity. Your decision variables should be the amount of Moisturizing+ and StandardSoap you produce. Your constraints should include the relationships between the amounts of lotion, soap, and SpecialX used to make Moisturizing+ and StandardSoap. In addition, your constraints should also include the fact that the total donated StandardSoap must equal 500L.

Solver's response will suggest an optimal production mix for maximizing the monthly profit. It makes sense to follow Solver's suggested production mix if it meets your company's requirements and goals.

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Answer:

(0,12)

Step-by-step explanation:

You would multiply 4 x 3 and go up to (0,12) on the y axis.

Helping in the name of Jesus.

The area of the amount of pie the person has eaten is equal to the area of a sector with 45° central angle. The area is 6.28 square inches.

The area of the amount of pie the person has eaten can be found using the formula for the area of a sector, which is

A = (θ/360)πr²

where θ is the central angle of the sector (in degrees), r is the radius of the circle, and π is the constant pi.

In this case, θ = 45° (the arc length),

r = 4 inches (the radius of the pie), and

π = 3.14 (the constant pi).

Plugging these values into the formula, we get:

A = (45/360)π(4)²

Simplifying the equation, we get:

A = (0.125)π(16)

A = 2π

A = 6.28 square inches

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Answer:

  10.81 ft

Step-by-step explanation:

You want the length of the shortest ladder that will reach over a 2 ft high fence to reach a building 6 ft from the fence.

Relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

In the attached diagram, the ladder is show as line segment CD, intersecting the top of the fence at point B. The length of the ladder is the sum of segment lengths BD and CB.

Using the above trig relations, we can write expressions that let us find these lengths in terms of the angle at D:

  sin(D) = AB/BD   ⇒   BD = AB/sin(D)

  cos(D) = BG/CB   ⇒   CB = BG/cos(D)

Then the ladder length is ...

  CD = BC +CB = AB/sin(D) +BG/cos(D)

  CD = 2/sin(D) +6/cos(D)

The minimum can be found by differentiating the length with respect to the angle. This lets us find the angle that gives the minimum length.

  CD' = -2cos(D)/sin²(D) +6sin(D)/cos²(D)

  CD' = 0 = (6sin³(D) -2cos³(D))/(sin²(D)cos²(D)) . . . common denominator

  0 = 3sin³(D) -cos³(D) . . . . the numerator must be zero

Factoring the difference of cubes, we have ...

  0 = (∛3·sin(D) -cos(D))·(∛9·sin²(D) +∛3·sin(D)cos(D) +cos²(D))

The second factor is always positive, so the value of D can be found from

  ∛3·sin(D) = cos(D)

  D = arctan(1/∛3) . . . . . . . divide by ∛3·cos(D), take inverse tangent

  D ≈ 37.736°

  CD = 2/sin(37.736°) +6/cos(37.736°) = 3.51 +7.30 = 10.81 . . . feet

The shortest ladder that reaches over the fence to the building is 10.81 feet.

__

Additional comments

The second attachment shows a graphing calculator solution to finding the minimum of the length versus angle in degrees.

The ladder length can also be found in terms of the distance AD.

  L = BD(1 +BG/AD) = (1 +6/AD)√(4+AD²)

The minimum L is found when AD=∛(BG·AD²) = ∛24 ≈ 2.884.

The solution of equation x² = 30 will be √30 and -√30. And the solution of equation x³ = 30 is ∛30.

In other words, the collection of all achievable values for the parameters that fulfill the specified mathematical equation is the suitable repository of the bunch of equations.

The equations are given below.

x² = 30 and x³ = 30

From equation x² = 30, then we have

x² = 30

x = ±√30

x = +√30, -√30

From equation x³ = 30, then we have

x³ = 30

x = ∛30

The solution of equation x² = 30 will be √30 and -√30. And the solution of equation x³ = 30 is ∛30.

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Answer:

x=10

Step-by-step explanation:

solve for x: 1/2x+4=9

First, you need to get the variable x to be on a side of the equation, by itself. That is your goal throughout the problem. The easiest way to start this is by removing 4 from the left side of the equation. We know that before the number 4 is a plus sign. In order to remove 4 from the left side of the equation, we must do the opposite of the plus sign. The plus sign represents addition, and the opposite of addition is subtraction. This means we need to subtract 4 from the left side. Remember, that whatever we do to one side, we must do to the other side! This means we must subtract 4 on BOTH sides of the equation.

On the left side of the equation, we have 4 and we subtract it by 4.

4-4=0

Since the answer is 0 we can forget about the number, because it does not hold any value.

Next, on the right side of the equation we have 9, and we subtract it by 4, as well because whatever we do to one side, we must do to the other side.

9-4=5

Our new equation should be: 1/2x=5

Our last step is to continue our goal from the beginning of the problem; to get x alone on one side of the equation. In order to complete that goal, we must remove 1/2 from the left side of the equation. Remember when we subtracted 4 one each side, we took the opposite of the sign. In this equation, we don't necessarily see a sign like before. However, whenever x is directly beside another number, that means that it is being multiplied by that number. Just like how the opposite of addition is subtraction, the opposite of multiplication is division. We need to divide 1/2 on both sides.

On the left side, we divide 1/2x by 1/2.

1/2 divided by 1/2 is 10

One isn't necessary to keep in the equation ONLY if it is next to x, like in this case.

Lastly, whatever we do to one side, we must do to the other. We finish the problem by dividing 5 by 1/2.

5 divided by .5 is 10

We are left with x=10.

The answer is 10.

The solution of the given quadratic system above would be = 6 , -10 for X and y respectively. That is option B.

To calculate the value of x and y substitution method should be used.

3x + y= 8 ---> equation 1

y=-x² + 3x + 8 ---> equation 2

Make y the subject of formula in equation 1;

y = 8 - 3x

Substitute y = 8 - 3x into equation 2;

8 - 3x = -x² + 3x + 8

x² = 3x +3x +8 -8

x² = 6x

X = 6

Substitute X = 6 into equation 1;

3(6) + y = 8

Make y the subject of formula;

y = 8-18

y = -10

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We can rewrite y=[tex]5e^{-0.7t}[/tex] using the properties of exponents as follows:

y=[tex]5e^{-0.7t} =5(e^{-0.7)t} =5(\frac{1}{e^{0.7} })t[/tex]

We can recognize [tex]\frac{1}{e^{0.7} }[/tex] as a base for exponential function that can be written in the form 1 ±r We know that is an increasing function, so [tex]e^{0.7}[/tex]≥1

therefore [tex]\frac{1}{e^{0.7\\} }[/tex]≥1 which means we must use the form y=a[tex](1-r^){t}[/tex]

To find the percent rate of change, we can use the formula:

percent rate of change=|r|×100

So, the percent rate of change is:

=|0.503|×100

Rounding to the nearest tenth of a percent, we get a percent rate of change of approximately 50.3%.

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