Exponential Growth Functions: Assignment

Which graph represents the function f(x) =3/2(2)x?

D. Graph 4

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

3

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?

C. The graph will show an initial value that is lower on the y-axis.

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?

C. f(x) = 1500(2.15)^x

Use the fact that the bacteria is doubling every five minutes. What fraction of the bottle was full at 11:20 a.m.?

D. 1/16

If the cells continue to double every 5 minutes, how long will it take to fill 3 additional bottles of the same size?

10 minutes

At 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. At 10:15 a.m., there are 8 cells in the bottle. At what time will there be 16 cells in the bottle? At what time will there be 64 cells in the bottle?

1. 10:20 AM 2. 10:30 AM

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

1. 240 2. 1.16

The bottle is completely full at 11:40 a.m. Which statements help explain this result? Check all that apply.

1. The bottle was 1/2 full at 11:35 a.m. and doubled again after 5 minutes. 2. The bottle was 1/4 full at 11:30 a.m. and doubled twice after 10 minutes. 4. Exponential growth involves a constant multiplicative rate of change.

Which statements are true of the function f(x) = 3(2.5)x? Check all that apply.

1. The function is exponential. 3. The function increases by a factor of 2.5 for each unit increase in x. 4. The domain of the function is all real numbers.

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.

At 11:30 a.m. the bottle is 1/4 of the way full. At what time will the bottle be 1/2 full?

B. 11:35 a.m.

A table representing the function f(x) = 2(3.2)^x is shown below. What is true of the given function?

B. The function increases at a constant multiplicative rate.

At 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. How many cells will be in the bottle at 10:15 a.m.?

C. 8

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 Answer: 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.

The bacteria took 1 hour and 40 minutes to fill the initial bottle. Explain how it only took 10 minutes to fill 3 additional empty bottles.

Sample Answer: The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.

This graph models the exponential growth of the strain of bacteria. What does the ordered pair (15, 8) represent?

There are 8 bacteria cells are 15 minutes.