Find a formula for the population, P=f(t)

Question

 P=f(t) gives the size of a population that begins with 15,000 members and grows at a continuous annual rate of 1.91%.   

Find a formula for the population,  P=f(t)

 (do not include any commas in your formula)

Answer 1

The formula for the population is P = 15000e^(0.0191)t.

Since we know that the population grows at a continuous annual rate, we can use an exponential model for this situation, where f(t) = Pe^rt, where f(t) is the amount of population in t years, P is the initial population, e is the exponential constant, r is the annual growth rate, and t is the time in years.

Since we know that the initial population is 15,000 and the growth rate is 1.91%, we can subsitute those values so that f(t) = 15000e^(0.0191)t, and since P = f(t), P = 15000e^(0.0191)t.