A biologist is comparing the growth of a population of flies per week to the number of flies an lizard will consume per week. He 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, he has observed that the iguana cannot eat more than eight flies in one week. Explain to the biologist how he can solve this on a graph using a system of equations. Identify any possible constraints to the situation.

Question

A biologist is comparing the growth of a population of flies per week to the number of flies an lizard will consume per week. He 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, he has observed that the iguana cannot eat more than eight flies in one week.  Explain to the biologist how he can solve this on a graph using a system of equations. Identify any possible constraints to the situation.

sodapop · Answer

@phi @Jim766

anonymous · Answer

Well, to begin with, you have two equations modeling two related things:
$$\text{population: }p(x)=3^x\
\text{consumption: }c(x)=5x-1$$
The solution to this system would be the intersection of the equations, when $p(x)=c(x)$.

To solve by graphing, you would plot both equations and find the intersection point.

The constraint would be that $c(x)\le8$, since the iguana can't consume more than eight flies.