Question

Use a graph and table to predict when the population will drop below 8,000

Answer 1

PART 1

The exponential decay model is given to be:

$y=a(1-r)^x$

where a is the initial value and r is the decay rate.

In the question, the initial value is 15,500 and drops at a rate of 3%. This means that we have the following parameters:

$\begin{gathered} a=15500 \\ r=\frac{3}{100}=0.03 \\ \therefore \\ 1-r=1-0.03=0.97 \end{gathered}$

Therefore, the exponential model is gotten to be:

$y=15500(0.97)^x$

PART 2

The graph of the function is shown below:

At x = 8000, we have the time as shown below:

The time will be 21.7 years.