Exponential functions

Given:

A population numbers 15,000 organisms initially and grows by 19.7 % each year.

Let P represents the population.

Let t be the number of years of growth.

An exponential model for the population can be written in the form of

We need to determine the exponential model for the population.

Exponential model:

An exponential model for the population is given by

where a is the initial value and

and b is the rate of change.

From the given, the value of a is given by

Also, the value of b is given by

Thus, substituting the values of a and b in the exponential model, we get;

Thus, the exponential model for the given population is

0 is its x and y coordinate