The population P of a small town, measured in hundreds, is modeled by the inverse of the function P−1(t) = 10ln(50t − 1000), where t is measured in years. Find the equation to model the population and determine its initial value.

P = 5t +100 where P(0) = 100
P = 1/50 In(0.1t)+20
P = 1/500e^t + 20
P = 1/50e^0.1t + 20

Answers

Answer 1

Using the inverse function, it is found that the equation is:

[tex]P(t) = \frac{e^{0.1t}}{50} + 20[/tex]

It's initial value is 20.

---------------------------

We want to find the inverse of:

[tex]y = P^{-1}(t) = 10\ln{50t - 1000}[/tex]

To do this, we exchange y and t, and isolate y.

Then:

[tex]10\ln{50y - 1000} = t[/tex]

[tex]\ln{50y - 1000} = \frac{t}{10}[/tex]

[tex]e^{\ln{50y - 1000}} = e^{0.1t}[/tex]

[tex]50y - 1000 = e^{0.1t}[/tex]

[tex]50y = e^{0.1t} + 1000[/tex]

[tex]y = \frac{e^{0.1t} + 1000}{50}[/tex]

[tex]y = \frac{e^{0.1t}}{50} + \frac{1000}{50}[/tex]

[tex]P(t) = \frac{e^{0.1t}}{50} + 20[/tex]

It's initial value is:

[tex]P(0) = \frac{e^{0.1(0)}}{50} + 20 = 0.02 + 20 = 20.02[/tex]

Rounding, 20.

A similar problem is given at https://brainly.com/question/23950969

Answer 2

Answer:

P = 1/50e^0.1t + 20

Step-by-step explanation:


Related Questions

WILL GIVE BRAINLIEST!!!!!!!
A surveyor wants to find the distance between peaks A and B. He finds point C, 288 ft from peak A, so that ACB is a right angle. The measure BAC is 89. Find the distance AB

Answers

Hints on solving trigonometry problems:

If no diagram is given, draw one yourself.

Mark the right angles in the diagram.

Show the sizes of the other angles and the lengths of any lines that are known

Mark the angles or sides you have to calculate.

Consider whether you need to create right triangles by drawing extra lines. For example, divide an isosceles triangle into two congruent right triangles.

Decide whether you will need Pythagorean theorem, sine, cosine or tangent.

Check that your answer is reasonable. The hypotenuse is the longest side in a right triangle.

How to use the tangent ratio to find missing sides or angles?

Example:

VI.
Molly paid $85 last month for her utilities. 55% of this amount was for electricity
a. How much did Molly pay for electricity?
What percentage of her money did she have left over?
c. What is the amount of leftover money Molly has for last month?

Answers

Answer:

$46.75

0.55 X 85 = $46.75

Raquel has to fill-up 5 volleyball with air. Each ball has a radius of 4.5 inches. What is the volume of the 5 volleyballs all together?

WILL MARK BRAINLEST!!

Answers

Answer:

Mate just divide 5 by 4.5 and you got your answer (1.11)

Step-by-step explanation:

If you see any question that has each in its name then its a division question.

PLEASE HELP!! I don't really know how to solve this.

Answers

Answer:

x=13

y=14

Step-by-step explanation:

We know that angle JNK is equal to angle MNL. We also know that angle JNK and angle KNL are supplementary.

Knowing this, we can write two equations: [tex]4x-1=3y+9[/tex] and [tex](4x-1)+(2x+6y+19)=180[/tex]. We can solve for y in the first equation. Subtracting 9 from both sides gives us [tex]4x-10=3y[/tex]. Dividing both sides by 3 gives us [tex]\frac{4x-10}{3} =y[/tex].

We can plug that in to the second equation to get [tex](4x-1)+(2x+6(\frac{4x-10}{3} )+19)=180[/tex]. Expanding the second parenthesis, we get [tex]2x+8x-20+19[/tex] which equals [tex](10x-1)[/tex]. We now have [tex](4x-1)+(10x-1)=180[/tex]. Expanding gives us [tex]14x-2=180[/tex]. Adding 2 to both sides gives us [tex]14x = 182[/tex]. Dividing both sides by 14 gives us [tex]x=13[/tex].

We can now plug 13 into the above equation to solve for y. [tex]y= \frac{4*13-10}{3}[/tex] Solving that gives you [tex]y=14[/tex].

Plz help me I will give you 40 points and Brainly

Answers

I’m not 100% but I think it could be the last table

What is the volume of the cylinder shown? (Use 3.14 for it.)


6.838.92 in.^3

1.413.56 in^3

1.243.44 in^3

11.190.8 in.^3

Answers

Step-by-step explanation:

11^2= 121

multiply by pi

121×3.14=379.94

then multiply the height

379.94×18=6,838.92

help please. need it asap

Answers

Answer:

x = 180 - 50 - 86 = 44°


4)Greg's backyard is 47 feet wide. How many yards and feet is this

Answers

Answer: 15 Yards 2 feet

Step-by-step explanation:

3 feet in a yard

45/3 = 15

2 remaining = 2 feet

Answer:

15.667 in yards

Step-by-step explanation:

Determine the value of variable in the following
equation:
2x + 40 = 30

Answers

Answer: x = -5

Steps:
2x + 40 = 30
2x = 30 - 40
2x = -10
x = -10 / 2
x = -5
I believe the answer is x=-5

Heyyy...need ur help...again cause I'm uneducated

Answers

Answer:

c

Step-by-step explanation:

Answer:

A and D

That is the answer.

Question 6 of 10
A(n) is produced when you slice a cone with a plane that is parallel to
the base of the cone.
A. parabola
Ο Ο Ο
B. circle
C. hyperbola
D. ellipse
SUBMIT

Answers

So it is B! Good luck

The correct option is (b) circle .

The conic section formed by the cone and a plane parallel to its base is a circle.The surface of a right-regular cone and a plane parallel to the base of the cone cross to form the closed figure known as a circle. The ellipse, which we'll discuss next, is actually just a special instance of the circle.

What is conic?Any curve created by the intersection of a plane and a right circular cone is known in geometry as a conic section, sometimes known as a conic. The intersection can be a circle, an ellipse, a hyperbola, or a parabola, depending on the angle the plane makes with the cone.

What conic section is formed from slicing parallel to the base of the cone ?

The resulting curve is a circle if the cone is cut in half parallel to the base. The curve is known as an ellipse if the cone is cut at a modest angle. The curve generated is known as a parabola if the slice is done parallel to the cone's edge.

Learn more about Conic brainly.com/question/22337165

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Help someone I just need the answer

Answers

there is no question

Help please I’m so behind

Answers

Answer: 5 and 27 as remainder

Step-by-step explanation:

4. Calculate the compound interest earned when $8 500 at 8% per year for:
a. 3 years
b. 8 months

Answers

i’m going to say a.3 years something is telling me it’s tht

The bus travels 35 blocks in 7 minutes . If the bus travels at a constant speed , how long will it take to travel 50 blocks ?



HELPPP PLEASE NOOO LINKSSS PLEASE

Answers

Answer:

10 min

Step-by-step explanation:

35/7=5 blocks in 1 min

50/5=10

In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearest
tenth of a cm, how long is that leg?

Answers

Answer:

36.5 cm

Step-by-step explanation:

The Adjacent leg is 36.5 cm

What are trigonometric functions?

"The trigonometric functions (also called circular functions, angle functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths."

What is hypotenuse, opposite and adjacent side of a right angled triangle?

"In a right angled triangle, the hypotenuse is the longest side, an opposite side is the one across from a given angle, and an adjacent side is next to a given angle."

We have

Hypotenuse (AB) = 58 cm

Angle θ = 51 degree

From the figure, by using trigonometric functions

Cos θ = [tex]\frac{BC}{AB}[/tex]

we have to find BC

Cos [tex]51^{0}[/tex] = [tex]\frac{BC}{AB}[/tex]

We have, AB = 58 cm

BC = AB cos [tex]51^{0}[/tex]

⇒BC = 58 . cos [tex]51^{0}[/tex]

⇒BC = 36.50 cm

⇒BC = 36.5 cm

Hence, Adjacent leg is 36.5 cm

Learn more about trigonometric functions here

https://brainly.in/question/1013629

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Adam is thinking of a mystery number. If he divides it by 9 and then subtracts 7 from it, the result is 1. What is Adam's mystery number?

Answers

Answer:

72

Step-by-step explanation:

1+7=8

8*9+72

Find the surface area of the cylinder
8 cm
3 cm
The surface area of the cylinder is cm?
(Simplify your answer. Type an exact answer in terms of r.)
Enter your answer in the answer hoy

Answers

Answer:

V=pr²t

=3,14 ×8×8×3

=602.88

Step-by-step explanation:

IVA

Answer: surface area

A = 56 π cm^2

Step-by-step explanation:

A = 56 π cm^2

you can stop here and write our answer as 56π Or we can plug in 3.14 and multiply. 56*3.14 = 175.84cm^2

What is the recursive rule for an=4n-3

Answers

Answer:

1

Step-by-step explanation:

n=1

4×1=4

4-3=1

a trucker hauls citrus fruit from Florida to Montreal. Each crate of oranges is 4 ft3 in volume and weighs 80 lb. Each crate of grapefruit has a volume of 6 ft3 and weighs 100 lb. His truck has a maximum capacity of 300 ft3 and can carry no more than 6800 lb. Moreover, he is not permitted to carry more crates of grapefruit than crates of oranges. If his profit is $2.50 on each crate of oranges and $4 on each crate of grapefruit, how many crates of each fruit should he carry for maximum profit

Answers

answer = 560 profited

Jessie saves $6 each week. In how many weeks will she have saved at least $50?

Answers

Answer:

9 weeks at least to have at least 50 dollars.

Step-by-step explanation:

Well 6 dollars each week and to get AT LEAST 50 dollars you need to save for 9 weeks.

Well 9*6=54

If you do it for 8 you’d only get 48 which is not at least 50 but 54 is.

So 9 weeks is the final answer.

50≤54

50 isn’t less then 48

Answer

.      .      .        .             .            .

Step by step explanation -

can someone help me plss

Answers

The answer is 3!! Hope this helps

Help! find the area of the parallelogram

Answers

28.2

Step-by-step explanation

A=bh=6·4.7≈28.2

The price of the stereo was $96 the tax rate was 6% what was the tax

Answers

Answer:

101.76

Step-by-step explanation:

If 25% is 14, what is 100%?

Answers

Answer:

56

Step-by-step explanation:

25% = 14

Therefore,

25%*4 = 14*4

100% = 56

What is the graph of the system y = −2x + 3 and 2x + 4y = −8? Line through point 0, 3 and 1, 1. Line through 0, negative 2 and negative 4, 0. Line through point 0, 3 and 1, 1. Line through 0, 2 and negative 4, 0. Line through point 0, 3 and 1, 1. Line through 0, 2 and 4, 0. Line through point 0, 3 and 1, 1. Line through 0, negative 2 and 4, 0.

Answers

Answer:

X = -4-2y

Step-by-step explanation:

Answer:

Line through point 0, 3 and 1, 1. Line through 0, negative 2 and negative 4, 0.

Step-by-step explanation:

I accidentally got it right

Which image shows the position of
2
n a number line?
ОА
2
-1
0
1
OB.
th
1
-1
-3
- 2
2
3
Ос.
-2
0
-3
1
2
3
D.
+
-2
- 1

Answers

Answer:

b

Step-by-step explanation:

HELPP !!! I need help

Answers

Imy ding guardian guardian Angel

Answer:

4. the answer is 5.4 which is between 5 and 6.

5. the answer is C.

Step-by-step explanation:

for #4 you just had to divide 27 by 5, and for #5 both numbers are positive so they are in the first quadrant.    

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Lesson 5.16 - Problem Solving with Mixed Numbers (D)
QULZ
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Problem Solving with Mixed Numbers
Jada made 3 1/6gallons of lemonade. Jada served 5/6
gallon to her friends.
How much lemonade does Jada have left?
Enter your answer as a mixed number in simplest form by filling in the boxes.


Answers

Answer:

Try Reasearching it! I hope you have a fantastic day/night ;-;

Step-by-step explanation:

Please help I don't understand this subject in math and my teacher isn't explaining it well. please explain how you find the answer, thanks :)​

Answers

Answer:

[tex]in \: this \: shape \: you \: have \: two \: pieces \: one \: square \: ad \: half \: of \: circle \\ area \: of \: circle = 12 \times 12 = 144 \\ area \: of \: hafl \: of \: circle = 12 \times 12 \times 0.25 \times 3.14 = 113.04 \\ whole \: area = 144 + 113.04 = 257.04[/tex]

Answer: E. 200.5 ft

so first you’d find the area of the square which is 12 x 12 = 144 (area = length x width)

next, find the radius of the semi circle which is 12 divided by 2 (because we used the measurements from the square and the diameter is 12 and radius is half of diameter)

pretend your solving for a full circle and then divide it by 2 to get the answer for the semi circle since a semi circle is half of a circle (formula for circle A = pi r^2)

area of circle = 113.04 divided by 2 to get semi circle = 56.5

then add both areas together

56.52 + 144 = 200.5

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