At the beginning of an experiment, the number of bacteria in a colony was counted at time t = 0. The number of bacteria in the colony t minutes after the initial count is modeled by the function f(t) = 4(2)t. Which value and unit represent the average rate of change in the number of bacteria for the first 5 minutes of the experiment?

I. 20
II. 24.8
III. minutes per bacteria
IV. bacteria per minute
A) I only
B) I & III
C) II only
D) II & IV

Option D: II and IV represents the average rate of change in the number of bacteria for the first 5 minutes in the experiment

Explanation:

Given that the number of bacteria in the colony t minutes after the initial count is modeled by the function

We need to determine the value and unit that represent the average rate of change in the number of bacteria for the first 5 minutes of the experiment.

The rate of change of bacteria can be determined using the slope formula.

The number of bacteria at time is given by

The number of bacteria at time is given by

The average rate of change is given by

Substituting the coordinates and , we have,

Thus the average rate of change is 24.8 bacteria per minute.

Therefore, Option D is the correct answer.