The base of the exponential function (1.75) is greater than 1, this represents exponential growth. As x increases, the value of the function will grow at an increasing rate.
Describe Exponential Growth?Exponential growth is a mathematical concept that describes a process where a quantity grows at an increasing rate proportional to its current value. In other words, the larger the quantity, the faster it grows. This leads to a graph that is characterized by a rapid upward curve that becomes steeper and steeper over time.
Exponential growth is often represented by the equation y = abˣ, where y is the final amount, a is the initial amount, b is the growth factor or base, and x is the time or number of periods.
The function f(x) = a(1+r)ˣ represents exponential growth, where "a" is the initial value, "r" is the growth rate as a decimal, and "x" is the time variable.
In this case, the initial value is 50, and the growth rate is 75%, or 0.75 as a decimal. Therefore, the equation for the function becomes:
f(x) = 50(1+0.75)ˣ
Simplifying this expression, we have:
f(x) = 50(1.75)ˣ
Since the base of the exponential function (1.75) is greater than 1, this represents exponential growth. As x increases, the value of the function will grow at an increasing rate.
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A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $80,000 saved up for when she goes to college in 15 years, assuming the account earns a 6% return.
Annual deposit: $
We can use the future value formula for an annuity to solve this problem:
FV = PMT * ((1 + r)^n - 1) / r
where:
FV is the future value of the annuity
PMT is the regular payment or deposit
r is the annual interest rate
n is the number of periods (in this case, the number of years)
We want to solve for PMT, so we can rearrange the formula to get:
PMT = FV * r / ((1 + r)^n - 1)
Plugging in the given values, we get:
FV = $80,000
r = 6% = 0.06
n = 15 years
So, the annual deposit required is:
PMT = $80,000 * 0.06 / ((1 + 0.06)^15 - 1) ≈ $3,782.58
Therefore, the man would need to deposit approximately $3,782.58 into the account each year in order to have $80,000 saved up for his granddaughter's college education in 15 years, assuming a 6% return.
(Score for Question 3: of 5 points) 1. a). Find the inverse of the function, f(x) = (x - 2)3 - 3. Please show all work in finding the inverse Answer: b) Now graph the inverse function f-1 (x) using the equation you found as the answer to part a) No computer-generated graphs will be accepted. Remember to clearly indicate at least three (3) points on the graph
The inverse of function is (x + 3)^(1/3) + 2 and the graph is attached below
What is the inverse of the functiona) To find the inverse of the function f(x) = (x - 2)^3 - 3, we can follow these steps:
1. Replace f(x) with y: y = (x - 2)^3 - 3
Solve for x in terms of y:
a. Add 3 to both sides: y + 3 = (x - 2)^3
b. Take the cube root of both sides: (y + 3)^(1/3) = x - 2
c. Add 2 to both sides: x = (y + 3)^(1/3) + 2
Replace x with f^-1(x): f^-1(x) = (x + 3)^(1/3) + 2
b) To graph the inverse function f^-1(x), we can use the equation we found in part a) and plot some points:
When x = 0, f^-1(x) = (0 + 3)^(1/3) + 2 = 3^(1/3) + 2When x = 1, f^-1(x) = (1 + 3)^(1/3) + 2 = 2^(1/3) + 2When x = 3, f^-1(x) = (3 + 3)^(1/3) + 2 = 2 + 2 = 4So we have three points: (0, 3^(1/3) + 2), (1, 2^(1/3) + 2), and (3, 4).
To sketch the graph, we can also note that the function f(x) = (x - 2)^3 - 3 has a vertical asymptote at x = 2 and a local minimum at (2, -3). Therefore, the inverse function f^-1(x) will have a horizontal asymptote at y = 2 and a local maximum at (4, 2).
Combining all of this information, we can sketch the graph of f^-1(x) as shown below:
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Jan bought 7 liters of orange juice how many milliters did she buy
Answer:
The answer you're looking for is 7000ml
Step-by-step explanation:
Since there are 1000 millimeters inside a liter we can use the equation
x = 7×1000.
We need to first simplify all terms giving us this equation
x = 7000
With that, we are finished and that's how you do this question.
I hope this was helpful!
A researcher is investigating academic motivation among college students and their siblings. This type of study would be _______
Answer:
This type of study would be a comparative study, as it involves comparing the level of academic motivation between college students and their siblings.
Step-by-step explanation:
please help me :(
use the Remainder Theorem and synthetic division please
The value of the functions are,
⇒ f (- 10) = 20201
⇒ f (2) = 17
⇒ f (3) = 143
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The value of function is,
⇒ f (x) = 2x⁴ + x² - 10x + 1
Now, We can find all the values as;
At x = - 10;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (- 10) = 2 (- 10)⁴ + (- 10)² - 10 (- 10) + 1
⇒ f (- 10) = 20000 + 100 + 100 + 1
⇒ f (- 10) = 20201
At x = 2;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (2) = 2 (2)⁴ + (2)² - 10 (2) + 1
⇒ f (2) = 32 + 4 - 20 + 1
⇒ f (2) = 17
At x = 3;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (3) = 2 (3)⁴ + (3)² - 10 (3) + 1
⇒ f (3) = 162 + 9 - 30 + 1
⇒ f (3) = 143
Thus, The value of the functions are,
⇒ f (- 10) = 20201
⇒ f (2) = 17
⇒ f (3) = 143
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- A state fair uses 32 pallets of lemons for lemonade and 32 pallets for
lemon ice. Which uses a greater amount of lemons?
Answer:
- A state fair uses 32 pallets of lemons for lemonade
Step-by-step explanation:
Write the ratio as a fraction in lowest terms. 44 minutes to 5 hours
Answer:Let's convert hours to minutes:
Now we have:
44 minutes to 300 minutes
We write the ratio as a fraction:
We can reduce both the numerator and denominator by 4, to get:
The correct answer is:
Step-by-step explanation:
Yesterday, a movie theater sold 290 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $566 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.
PLEASE HELP
Answer:
Step-by-step explanation:
Let's call the number of large bags of popcorn sold "L" and the number of small bags of popcorn sold "S".
We can set up two equations based on the information given:
L + S = 290 (the total number of bags of popcorn sold)
4L + S = 566 (the total revenue from popcorn sales)
We can use substitution or elimination to solve for L and S.
Substitution:
From the first equation, we know that S = 290 - L. We can substitute this into the second equation:
4L + (290 - L) = 566
Simplifying, we get:
3L + 290 = 566
3L = 276
L = 92
Then we can use the first equation to find S:
L + S = 290
92 + S = 290
S = 198
So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.
Elimination:
We can eliminate one variable by multiplying one of the equations by a constant to make the coefficients of one of the variables equal but with opposite signs.
In this case, we can multiply the first equation by 4 to make the coefficients of S equal but with opposite signs:
4L + 4S = 1160
4L + S = 566
Subtracting the second equation from the first, we eliminate L:
3S = 594
S = 198
Then we can use either of the original equations to find L:
L + S = 290
L + 198 = 290
L = 92
So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.
What are the measures of all angles of a isosceles triangle.
Answer:
The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
Step-by-step explanation:
4. 6.9B Luke is about to start cooking. He places some butter in a pan and heats up the pan. As the pan heats up, the butter begins to melt. How is the energy moving? The cold is moving from the pan and into the butter The cold is moving from the butter and into the pan The heat is moving from the pan and into the butter The heat is moving from the butter and into the pan
As the temperature of the pan increases, the heat transfer from the butter to the pan increases, causing the butter to melt faster. Ultimately, this heat transfer is necessary for Luke to prepare his food. Without it, the butter would stay solid and would not cook properly.
What is heat transfer?Heat transfer is the transfer of energy from one place to another due to a difference in temperature. Heat transfer can occur through conduction, convection, and radiation. Heat is always transferred from hotter to colder objects and the rate of transfer depends on the temperature difference between the two and the material it is passing through. Heat transfer is essential in many natural and man-made processes.
The energy is moving in two directions. Cold is moving from the pan and into the butter, while the heat is moving from the butter and into the pan. This is known as a heat transfer. Heat transfers occur when two objects at different temperatures come into contact with each other. In this case, the cold pan is coming into contact with the warm butter, causing the heat to move from the butter and into the pan. This heat transfer causes the butter to melt. As the temperature of the pan increases, the heat transfer from the butter to the pan increases, causing the butter to melt faster. Ultimately, this heat transfer is necessary for Luke to prepare his food. Without it, the butter would stay solid and would not cook properly.
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I need help with choosing the correct answer for the second part of A.) this is a Elementary Statistics homework problem
50 Points!!! Write a verbal sentence to represent 5n/n+3=n-8. Show as much work as possible please. Photo attached. (Only looking for answer to 12B)
Answer: Your welcome!
Step-by-step explanation:
5n / (n + 3) = n - 8
5n = n(n + 3) - 8(n + 3)
5n = n^2 + 3n - 8n - 24
n^2 - 5n - 24 = 0
n = 4 or n = -6
The verbal sentence to represent 5n/n+3=n-8 is "When n is 4 or -6, 5n divided by n plus 3 is equal to n minus 8."
A box contains 8 green marbles and 17 white marbles. If the first marble chosen was a green marble, what is the probability of choosing, without replacement, a white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
Step-by-step explanation:
[tex]\frac{17}{25}[/tex]
1354.24 rounded to the nearest tenth
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
It is true that the graph contains the point (0, 0).
The following three assertions regarding the function and its graph are true:
The function's graph resembles a parabola.
The graph begins at the bottom.
The point is shown in the graph (0,0).
Explanation:
A second-degree polynomial function, the quadratic function f(x) = x2 - 5x + 12 has a parabola as its graph.
The parabola widens downward because the coefficient of x2 is positive (1 in this instance).
When we replace x with -10 in the given function, we obtain the value of f(-10) as (-10)2 - 5(-10) + 12 = 82. Hence, "f(-10) = 82" is true.
We substitute x = 20 in the given function, resulting in f(20) = 202 - 5(20) + 12 = 212, to see if the point (20, -8) is on the function's graph. The claim "The graph contains the point (20, -8)" is untrue since the point's y-coordinate is -8, which is not equivalent to f(20).
We substitute x = 0 in the given function to get f(0) = 02 - 5(0) + 12 = 12 to determine if the point (0, 0) is on the function's graph. The assertion "The graph contains the point (0, 0)" is true because the y-coordinate of the point (0, 0) is 0, which is equivalent to f(0).
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Directions - Evaluate the following exponential function for the x-values in the table. Complete the table with y-values.
y=9x( 3/1 ) x
Some numeric values of the exponential function y = 9(3)^x are given as follows:
x = -2, y = 1.x = -1, y = 3.x = 0, y = 9.x = 1, y = 27.x = 2, y = 81.How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is given as follows:
y = 9(3)^x.
Hence some numeric values of the function are given as follows:
x = -2, y = 1. -> y = 9 x (3)^(-2).x = -1, y = 3. -> y = 9 x (3)^(-1).x = 0, y = 9. -> y = 9 x (3)^(0).x = 1, y = 27. -> y = 9 x (3).x = 2, y = 81. -> y = 9 x (3)^(2).Learn more about the numeric values of a function at brainly.com/question/28367050
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A service that repairs air conditioners sells maintenance agreements for $75 a year. The average cost of repairing an air conditioner is $350 and 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair. Find the service’s expected profit.
The service's expected profit is $6,800.
What is the basic arithmetic operations?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find the service's expected profit, we need to calculate the total revenue and the total cost, and then subtract the cost from the revenue.
First, let's calculate the total revenue. The service sells maintenance agreements for $75 a year, so for every 100 customers, the revenue will be:
100 customers x $75/customer = $7,500
Now, let's calculate the total cost. We know that 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair, and the average cost of repairing an air conditioner is $350. So for every 100 customers, the cost of repairs will be:
2 customers x $350/customer = $700
Finally, let's calculate the expected profit:
Expected profit = Total revenue - Total cost
Expected profit = $7,500 - $700
Expected profit = $6,800
Hence, the service's expected profit is $6,800.
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The cost of 3 scarves is $86.25. What is the unit price?
In linear equation, $28.75 is the unit price .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
The cost of 3 scarves is $86.25
then,
the unit price is = $86.25/3 = $28.75
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Pencil boxes cost $15 each. Calculators cost $24 each. Kelly bought a total of 100 pencil boxes and calculators for $2130. How many pencil boxes did she buy?
Answer:
Step-by-step explanation:
Kelly bought a total of 1500 pencil boxes.
Terry takes a 800 mg Tylenol for his headache. Every hour that the Tylenol is in his system, a quarter of the medication dissolves in his body.
1. WRITE a function that models the amount of Tylenol in Terry’s body over time. Use x for hours, and y for the amount of Tylenol, in mg, remaining in the body.
2. When there is less than 100mg of medicine left in the body, it safe to take it again. HOW LONG will it take before Terry can take more medicine?
Therefοre, the sοlutiοn οf the given prοblem οf functiοn cοmes οut tο be Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.
What is functiοn?The curriculum fοr mathematics includes a wide range οf tοpics, such as numbers, numbers, and their cοmpοnents, as well as cοnstructiοn, building, and bοth actual and hypοthetical geοgraphic places. A wοrk discusses the relatiοnships between different variables that all wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that, when cοmbined, prοduce specific results fοr each input.
Here,
The functiοn can be written as fοllοws:
=> y = 800 * (0.25)ˣ
where y is the quantity οf Tylenοl still in Terry's system in milligrammes and x is the number οf hοurs since he last tοοk the medicatiοn.
When Terry's bοdy's cοncentratiοn οf Tylenοl gοes belοw 100mg, we need tο find οut hοw lοng it will be befοre he can take mοre medicatiοn.
The expοnential decay fοrmula frοm part 1 can be used tο find a sοlutiοn fοr this:
=> 800 * (0.25)ˣ = 100
by 800, divide bοth sides.
=> (0.25)ˣ = 0.125
Cοnsider the twο sides' lοgarithms:
=> lοg(0.25) * x = lοg (0.125)
tο find x:
=> lοg(0.125) / lοg (0.25)
=> x = 2.4
Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.
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In an examination, Julius scored 5 more marks than John who in turn scored 4 marks less than Grace. If the total mark scored by the three students was 150. Find the mark of each student?
Making linear equations for given scores, Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.
What is a linear equation, exactly?
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable, with the degree of each variable being 1. In other words, a linear equation is an equation of a straight line, which can be expressed in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept of the line. Linear equations are used to model relationships between variables that have a constant rate of change, such as distance traveled over time or cost per item.
Now,
Let's assume that Grace's score is x.
Then, John's score will be x-4.
And, Julius's score will be x-4+5 = x+1.
The sum of their scores is given as 150. So, we can write an equation as:
x + (x-4) + (x+1) = 150
Simplifying the equation, we get:
3x - 3 = 150
Adding 3 to both sides, we get:
3x = 153
Dividing by 3 on both sides, we get:
x = 51
So, Grace's score is x = 51.
John's score is x-4 = 47.
And, Julius's score is x+1 = 52.
Therefore,
Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.
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I plan to deposit their annual profits in an investment account earning a 9% annual return. If the owner starts with their first deposit today for $22,000 and expects to make the same profit for the next 7 years, how much will be saved for retirement at that point?
Answer: We can use the formula for future value of an annuity to calculate how much will be saved for retirement:
FV = Pmt x (((1 + r)^n - 1) / r)
where:
FV is the future value of the annuity
Pmt is the payment made each period (in this case, the annual profit of $22,000)
r is the annual interest rate (9% or 0.09 as a decimal)
n is the number of periods (7 years)
Substituting the given values into the formula, we get:
FV = $22,000 x (((1 + 0.09)^7 - 1) / 0.09)
FV = $22,000 x (1.9904 / 0.09)
FV = $22,000 x 22.116
FV = $485,552
Therefore, the amount saved for retirement after 7 years will be $485,552.
Step-by-step explanation:
A car travels at an average speed of 68 miles per hour. How long does it take to travel 357 miles?
If a car travels at an average speed of 68 miles per hour, it takes it 5 hours 15 minutes to travel 357 miles.
What is the average speed?The average speed is the unit rate.
The average speed is computed as the quotient of the total distance and the total time.
Conversely, the time is a function of the division of the total distance by the average speed.
The total distance traveled by the car = 357 miles
The average speed = 68 miles per hour (mph)
The time = Distance/Average speed = 357/68 = 5.25 hours
= 5 hours 15 minutes.
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Pleaseeee yelp meeeeee
Answer:
x ≤ 6.8
Step-by-step explanation:
1.25x + 6.50 ≤ 15
1.25x ≤ 8.5
x ≤ 6.8
So, the answer is x ≤ 6.8
Answer:
Below
Step-by-step explanation:
1.25x + 6.50 <= 15 SUBTRACT 6.50 from both sides of the equation
1.25x ≤ 8.50 DIVIDE both sides by 1.25
x ≤ 6.8
what is the exact circumference of a circle with a radius of 17mm (Answer options) 8.5
17
34
68
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=17 \end{cases}\implies C=2\pi (17)\implies C=34\pi[/tex]
7 men build a house in 300 days how many men .working in the same rate can build the house in 70 days
Answer:
30 men
Step-by-step explanation:
7 men x 300 days = 2100 man-days to build 1 house)
(2100 man-days/house) x (1 house/70 days) = 30 men
Multiply f and 7. Then add 9 in expression
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $50.
If they offer a 2-year extended warranty for $7, what is the company's expected value of each warranty sold? Round your answer to the nearest cent.
Answer:
The expected value of each warranty sold is $23.8.
pleaseee i need help.
use the Remainder Theorem and synthetic division, please.
Using Remainder Theorem and synthetic division, f(-10) = 191, f(2) = 1, f(3) = 34
What is synthetic division?
A polynomial's coefficients are split one by one in synthetic division.
The split polynomial's zero, which belongs in the box on the far left, has this value.
To use the Remainder Theorem and synthetic division to evaluate f(-10), f(2), and f(3) for the function[tex]f(x)=2x^2+x^2-10x+1[/tex], we can proceed as follows:
First, we need to perform synthetic division using -10, 2, and 3 as the divisors.
1) For f(-10):
The result of the division is 191, so f(-10) = 191.
2) For f(2):
The result of the division is 1, so f(2) = 1.
3) For f(3):
The result of the division is 34, so f(3) = 34.
Therefore, we have:
f(-10) = 191
f(2) = 1
f(3) = 34
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Can someone help me on this?
Answer:
X+15 is the answer..................