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 [tex]P=a \cdot b^t[/tex]
We need to determine the exponential model for the population.
Exponential model:
An exponential model for the population is given by
[tex]P=a \cdot b^t[/tex]
where a is the initial value and
and b is the rate of change.
From the given, the value of a is given by
[tex]a=15,000[/tex]
Also, the value of b is given by
[tex]b=\frac{19.7}{100}=0.197[/tex]
Thus, substituting the values of a and b in the exponential model, we get;
[tex]P=15,000 \cdot (0.197)^t[/tex]
Thus, the exponential model for the given population is [tex]P=15,000 \cdot (0.197)^t[/tex]
