Exponential Functions - Assignment

What is the multiplicative rate of change for the exponential function graphed to the left?

3

Leticia invests $200 at 5% interest. If y represents the amount of money after x time periods, which describes the graph of the exponential function relating time and money? A. The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time. B. The initial value of the graph is 200. The graph increases by a factor of 5 per 1 unit increase in time. C. The initial value of the graph is 500. The graph increases by a factor of 2 per 1 unit increase in time. D. The initial value of the graph is 500. The graph increases by a factor of 1.02 per 1 unit increase in time

A

Which statements are true of the function f(x) = 3(2.5)x? Check all that apply. A. The function is exponential. B. The initial value of the function is 2.5. C. The function increases by a factor of 2.5 for each unit increase in x. D. The domain of the function is all real numbers. E. The range of the function is all real numbers greater than 3.

A, C, D

Which graph represents the function f(x) =(2)x?

The fourth graph

A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to represent the number of birds after x years. Which values should she use for a and b?

A=240 b=1.16

A table representing the function f(x) = 2 is shown below. What is true of the given function? A. The function increases at a constant additive rate. B. The function increases at a constant multiplicative rate. C. The function has an initial value of 0. D. As each x value increases by 1, the y values increase by 1.

B

A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario? A. f(x) = 1500(1.15)x B. f(x) = 1500(115)x C. f(x) = 1500(2.15)x D. f(x) = 1500(215)x

C

The given graph represents the function f(x) = 2(5)x. How will the appearance of the graph change if the a value in the function is decreased, but remains greater than 0? A. The graph will increase at a slower rate. b. The graph will show a decreasing, rather than increasing, function. c. The graph will show an initial value that is lower on the y-axis. d. The graph will increase at a constant additive rate, rather than a multiplicative rate.

C

In exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1? How would the function change if the base of the exponent were between 0 and 1?

Sample Response: If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing. What you need to include: If the base were 1, the function would be constant. If the base were 1, the graph would be a horizontal line. If the base were between 0 and 1, the function would be decreasing.