Question

A biologist is comparing the growth of a population of flies per week to the number of flies a bullfrog will consume per week. She has devised an equation to solve for which day (x) the bullfrog would be able to eat the entire population. The equation is 2x = 3x - 1. However, she has observed that the bullfrog 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.

Answer 1

Is there any additional info? Why two x's? Should be an x and y

Answer 2

That's the whole question and that's why I'm confused :/

Answer 3

Well, let me do some sloppy maths here.

2x = 3x - 1
-x = -1
x = 1

So then plug x in

2(1) = 3(1) - 1
2 = 2

So it checks out okay.

But this makes no sense, because he will consume the entire population on day 1. Something is very wrong.

Answer 4

Well the bullfrog can't eat more than 7

Answer 5

Are you sure the equation isn't 2^x = 3x - 1? Check it again.

Answer 6

you're correct.

Answer 7

it's 2^x = 3x - 1

Answer 8

@Compassionate I still can't manage to understand this :/

Answer 9

Okay. Take 2^2 = 3x-1 and put it in two different equations.

y = 2^x and y = 3x - 1

You intersect at 1 and 3

Do you get where I'm going with this?

Answer 10

I get why we're splitting it into two different equations.

Answer 11

I'm pretty confused to be honest. (bad at math)

Answer 12

Okay, so you understand that we split it into two equations to simplify it. Right? Now simply graph each one.

Answer 13

can you "Explain to the biologist how she can solve this on a graph using a system of equations." I'm understanding the graphing, I just don't know what they want me to tell them.

Answer 14

We can solve x below
y=2x and y=3x−x
these = graphs give us the x(x)
So the intersection happens at x = 1 and x = 3
She said the bullfrog cannot eat more seven a day
So, it will only take him 1 day.

Answer 15

Thanks :)