A biologist is comparing the growth of a population of flies per week to the number of flies an iguana will consume per week. He has devised an equation to solve for which day (x) the iguana would be able to eat the entire population. The equation is 3x = 2x + 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 iguana will consume per week. He has devised an equation to solve for which day (x) the iguana would be able to eat the entire population. The equation is 3x = 2x + 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.

anonymous · Answer

I think you're supposed to set it up like 

3^x=y?
2x+1=8?

Other than that I don't know.

anonymous · Answer

@phi , @Preetha

askswatw260 · Answer

wouldn't you need to graph it?

phi · Answer

can you fix this equation ?
The equation is 3x = 2x + 1.
??

askswatw260 · Answer

get x on one side

anonymous · Answer

Oops, the equation is 3^x=2x+1, it didn't copy over right.

experimentx · Answer

probably you didn't copy it right again

phi · Answer

Using Geogebra (free software) , I get this graph

anonymous · Answer

Okay. That looks right, so what would the constraint be? That an iguana can only eat 8 flies a week?

askswatw260 · Answer

its an inequality

phi · Answer

I think people are saying your equation should have < or >  not an = sign in it.

anonymous · Answer

It has an equal sign in the problem, it says to be solved by a system of equations.

askswatw260 · Answer

you need 2 equations(inequalities)

anonymous · Answer

So how would you explain to the biologist how he can solve this on a graph using a system of equations. Identify any possible constraints to the situation ? @mathstudent55 @MathsPro @mathmale  @Mathmagic18

sleepyjess · Answer

It should have read:
$$3^{x}=2x+1$$
@Compassionate @cwrw238 @ganeshie8

sleepyjess · Answer

@mathmale

anonymous · Answer

Do you want to solve this equation
3^x = 2x+1 ?

anonymous · Answer

u know logarithms , reply

ganeshie8 · Answer

$ \large 3^x = 2x + 1 $

The system of equations for the given equation are :
$\large y = 3^x$
$\large y = 2x+1$

You can graph these two equations in geogebra or any other graphing program. The intersection points give the times at which both the equations will have same values - that is -  the days at which the population of flies equal the flies consumed by iguana.

ganeshie8 · Answer

The given constraint iguana cannot eat more than 8 flies is redundant(y=2x-1 curve cannot have a growth rate of more than 2) - I have ignored it. You can ask your teacher whats the purpose of that statement.

ganeshie8 · Answer

yw

ganeshie8 · Answer

Btw, the possible constraints are  `x > 0` as x represents the population of flies, so x cannot be negative. Can you think of any other constraints ?

anonymous · Answer

Hey, @ganeshie8

Could 8x = 0 be a possible constraint? If x represents the amount of flies that an iguana can eat per week.