Exponential Decay Functions

Which are true of the function f(x) = 49(1/7)x? Check all that apply.

- The domain is the set of all real numbers. - The range is y > 0. - As x increases by 1, each y-value is one-seventh of the previous y-value.

The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x) = 10(0.5)x. What is the multiplicative rate of change of the function?

0.5

Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function?

0.98

The table represents an exponential function. https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-29.png What is the multiplicative rate of change of the function?

3/4

The table represents an exponential function. https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-27.png What is the multiplicative rate of change of the function?

a 1/5

Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car's value?

a f(x) = 20,000(0.85)x

Which is an exponential decay function?

c f(x) = 3/2(8/7)-x

Which is the graph of f(x) = 3(2/3)^x?

d https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-31d.PNG

A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment?

a f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0

Which is the graph of f(x) = 100(0.7)x?

a https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-10a.png

The graph of f(x) = 2x is shown on the grid. https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-21.png The graph of g(x) = (1/2)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?

b https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-21b.png

Which is the graph of f(x) = 4(1/2)^x?

b https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-30b.PNG

Two exponential functions are shown in the table. https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-24.png Which conclusion about f(x) and g(x) can be drawn from the table?

The functions f(x) and g(x) are reflections over the y-axis.

Which table shows exponential decay?

a https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-04a.png

The table represents an exponential function. https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-28.png What is the multiplicative rate of change of the function?

c 0.5

Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?

c f(x) = 1,200(0.97)x

Which graph represents exponential decay?

c https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-01c.png

Chelsea is graphing the function f(x) = 20()x. She begins by plotting the initial value. Which graph represents her first step?

c https://media.education2020.com/evresources/3109/3109-07/3109-07-02/3109-07-02-assessment/3109-07-02-08c.png