A town has 800 people initially. Find the formula for the population of the town, P, in terms of the number of years, t, if the town shrinks at an annual rate of 13% a year.

Question

Quizplus · Accepted Answer

The formula for exponential decay is given by:
P(t) = P(0) * e^(-rt)
where P(0) is the initial population, r is the annual decay rate, t is the number of years, and e is Euler's number (approximately 2.71828).

In this case, P(0) = 800, r = 0.13 (13% annual decay rate), and t is the number of years. So the formula becomes:
P(t) = 800 * e^(-0.13t)

Therefore, the correct choice is C.

A Town Has 800 People Initially