At the beginning of an experiment, the number of bacteria in a colony was counted at time t=O. The number of bacteria in the colony t minutes after the initial count modeled by the function B(t)=9(3)^t. What is the average rate of change in the number of bacteria over the first 6 minutes of the experiment?

We have been given that the number of bacteria in the colony t minutes after the initial count modeled by the function [tex]B(t)=9(3)^t[/tex]. We are asked to find the average rate of change in the number of bacteria over the first 6 minutes of the experiment.

We will use average rate of change formula to solve our given problem.

[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]

Upon substituting our given values, we will get:

[tex]\text{Average rate of change}=\frac{b(6)-b(0)}{6-0}[/tex]

[tex]\text{Average rate of change}=\frac{9(3)^6-9(3)^0}{6}[/tex]

[tex]\text{Average rate of change}=\frac{9(729)-9(1)}{6}[/tex]

[tex]\text{Average rate of change}=\frac{6561-9}{6}[/tex]

[tex]\text{Average rate of change}=\frac{6552}{6}[/tex]

[tex]\text{Average rate of change}=1092[/tex]

Therefore, the average rate of change in the number of bacteria is 1092 bacteria per minute.