The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke0.08t where k is a constant and t is the time in years. If the current population is 22,000, in how many
Years is the population expected to be 55,000? Round to the nearest year.
A) 5 yr
B) 11 yr
C) 76 yr
D) 6 yr

Question

Quizplus · Accepted Answer

Given the population model P(t) = 1 + ke^0.08t, and the current population is 22,000, we first find the value of k. Substituting P(t) = 22,000 and solving for k gives us k = 21,999. To find when the population will be 55,000, we set P(t) = 55,000 and solve for t, which gives us approximately 11 years.

The Population of a Particular City Is Increasing at a Rate