Question

A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard would be able to eat the entire population. The equation is 7x = 3x + 4.

Explain to the biologist how she can solve this on a graph using a system of equations.

Answer 1

• 7^x=3x+4

Break into two parts

• y=3x+4
• y=7^x

Now graph and find the solution

Answer 2

• (-1.307, 0.079), (1, 7)

Explanation:

Given equation:

• 7ˣ = 3x + 4

To solve this, express each side of the equation as different function and find the intersection of graphs of those functions:

• y = 7ˣ
• y = 3x + 4

As per graph, the solution is:

• (-1.307, 0.079), (1, 7)