Question

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?

Answer 1

To calculate the average rate of change of the bacteria population over the first 6 minutes, we evaluate the function B(t) at t = 0 and t = 6, find the difference in B(t) values, and divide by the change in time to obtain an average rate of change of 1092 bacteria per minute.

Step-by-step explanation:

To calculate the average rate of change of the bacteria population over the first 6 minutes, we need to evaluate the function B(t) = 9(3)t at t = 0 and t = 6, and then use these values to compute the average rate of change. The average rate of change is given by the formula:

\[\text{Average Rate of Change} = \frac{\text{Change in B(t)}}{\text{Change in t}} = \frac{B(6) - B(0)}{6 - 0}\]

First, we find B(0):

B(0) = 9(3)0 = 9 \times 1 = 9

Then, we calculate B(6):

B(6) = 9(3)6 = 9 \times 729 = 6561

Now, we use these values to find the average rate of change:

\[\text{Average Rate of Change} = \frac{6561 - 9}{6 - 0} = \frac{6552}{6} = 1092\]

The average rate of change of the number of bacteria over the first 6 minutes is 1092 bacteria per minute.

Answer 2

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}=(f(b)-f(a))/(b-a)`

Upon substituting our given values, we will get:

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

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

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

`\text{Average rate of change}=(6561-9)/(6)`

`\text{Average rate of change}=(6552)/(6)`

`\text{Average rate of change}=1092`

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