Final answer:
To determine when the bacterial population exceeds 2317, one should divide 2317 by 1350, take the natural logarithm of the result, then divide that by 0.12 to solve for t (the time).
Step-by-step explanation:
The subject of this question pertains to the mathematical field of exponential growth, specifically as it relates to bacterial populations. In this case, the equation representing the population growth of the bacteria is given by p(t) = 1350e^0.12t.
In order to determine when the population exceeds 2317, we look for the time (t) when p(t) > 2317. This involves rearranging the given equation to solve for t. First, we divide both sides of our equation by 1350 so that e^0.12t > 2317/1350.
Then, we take the natural logarithm (ln) of both sides, resulting in 0.12t > ln(2317/1350). Finally, by dividing both sides by 0.12, we solve for t.
Please note, use a scientific calculator to calculate the natural logarithm value and divide it by 0.12 to yield the approximate time, t, in which the population exceeds 2317.
Learn more about Exponential Growth