Question

An initial population of 1,500 increases at an annual rate of 15%. Write an exponential function to model the population increase. Use the function to find the population after 15 years.

Answer 1

To model the population increase, use the formula P = P0 * (1 + r)^t, where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the number of years. The population after 15 years can be found by substituting t = 15 into the function.

Step-by-step explanation:

To model the population increase, we can use the formula for exponential growth.

The formula is P = P0 * (1 + r)^t, where P is the final population, P0 is the initial population, r is the annual growth rate (as a decimal), and t is the number of years.

In this case, the initial population is 1,500 and the annual growth rate is 15%. So the exponential function to model the population increase is P = 1500 * (1 + 0.15)^t.

To find the population after 15 years, we can substitute t = 15 into the function. P = 1500 * (1 + 0.15)^15