Question

There are 20 goldfish in a pond. Their population is increasing by 20% each year. The same pond has 100 minnows. The minnow population is increasing by 10 minnows each year. Make a graph to find the year that the two species of fish will have the same population. In what year will the fish populations be approximately the same?

Answer 1

Answer:

13.5 years.

Step-by-step explanation:

We know that exponential growth function is in form $y=a\cdot(1+r)^x$, where, a is initial value and r is growth rate in decimal form.

Population of goldfish after x years would be $y=20\cdot(1+0.20)^x$.

We know that a linear function is in form $y=mx+b$, where, b is initial value and m is slope.

Population of minnow after x years would be $y=100+10x$.

Graphing both equations, we will get our required graph as shown in the attachment.

Since both graphs intersect at $x=13.5$, therefore, in the 13.5 years both populations will approximate the same.

Answer 2

The graph is attached, showing the intersection point at 13.5 years and populations of 235.2 for each population.

We only consider the portion of the graph from x=0 on, since negative time is illogical.  Tracing the graph we get the intersection point.