Question

Select the correct graph and equation.A pond had an initial population of 120 fish. The number of fish is exponentially decreasing by one-fourth each year. If y represents the number of fish in the pond after x years, determine the graph of the solution set for this situation and the equation modeled by the graph.

Answer 1

In order to model this situation, let's use the following exponential equation:

$y=a\cdot b^x$

Since the initial population is 120, we have a = 120, and since the number of fish decreases by 1/4 each year, the value of b is 3/4.

So the equation is:

$y=120\cdot(\frac{3}{4})^x$

For x = 1, the value of y is equal to:

$y=120\cdot\frac{3}{4}=90$

Looking for the graph with the points (0, 120) and (1, 90), we have the bottom left graph as the correct one.