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user100 [1]
2 years ago
7

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 col

ony 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?
Mathematics
1 answer:
yan [13]2 years ago
8 0

Answer:

1092

Step-by-step explanation:

We have been given that the number of bacteria in the colony t minutes after the initial count modeled by the function B(t)=9(3)^t. 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.

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

Upon substituting our given values, we will get:

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

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

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

\text{Average rate of change}=\frac{6561-9}{6}

\text{Average rate of change}=\frac{6552}{6}

\text{Average rate of change}=1092

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

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