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<u>Given</u>:
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.
<u>Exponential model:</u>
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