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 3^{x} = 5x – 1. However, she has observed that the lizard cannot eat more than seven flies in one week.

Explain to the biologist how she can solve this on a graph using a system of equations. Identify any possible constraints to the situation.

**Solution:-**

Given equation is 3^{x} = 5x-1

we can plot the graph of y = 3^{x}

and y = 5x-1

after piloting the graph of both equations we found that both graphs are intersecting at two points, (0.577,1.885) and (2,9)

There is one condition in the questions that lizard cannot eat more than seven flies in the week,

In the second point we can see that it eat 9 flies which is out of the given condition ,

so only solution is (0.577,1.885)