Question

Exponential functions

Answer 1

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 $P=a \cdot b^t$

We need to determine the exponential model for the population.

Exponential model:

An exponential model for the population is given by

$P=a \cdot b^t$

where a is the initial value and

and b is the rate of change.

From the given, the value of a is given by

$a=15,000$

Also, the value of b is given by

$b=\frac{19.7}{100}=0.197$

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

$P=15,000 \cdot (0.197)^t$

Thus, the exponential model for the given population is $P=15,000 \cdot (0.197)^t$