A biologist is comparing the growth of a population of flies per week. She has devised an equation to solve for which day (x) the bullfrg would be able to eat the entire population. The equation is 2^x=3x-1. However, she has observed that the bullfrog can not 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.

Question

A biologist is comparing the growth of a population of flies per week.  She has devised an equation to solve for which day (x) the bullfrg would be able to eat the entire population.  The equation is 2^x=3x-1.  However, she has observed that the bullfrog can not 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.

anonymous · Answer

@SolomonZelman

solomonzelman · Answer

she can eat no more than 7 flies per week, so  $\normalsize\color{blue}{ y≤7x\LARGE\color{white}{ \rm    │  }}$,  where is the number of weeks, and y is the number of flies.   $\normalsize\color{blue}{ \LARGE\color{white}{ \rm    │  }}$
Are you sure that the equation is,   $\normalsize\color{blue}{ 2^x=3x-1\LARGE\color{white}{ \rm    │  }}$   ?

anonymous · Answer

Yes, I am

solomonzelman · Answer

But the only possible solution to that         (the  $\normalsize\color{blue}{ 2^x=3x-1\LARGE\color{white}{ \rm    │  }}$)      equation is 1.

solomonzelman · Answer

I am not sure how to go about    $\normalsize\color{black}{ 2^x=3x-1\LARGE\color{white}{ \rm    │  }}$

anonymous · Answer

I'm positive that's it... are you using the other equation we came up with as a system?

solomonzelman · Answer

So perhaps as phi said we just need it for one 1.

solomonzelman · Answer

one week*

solomonzelman · Answer

I am not sure about this, maybe @phi @IMStuck since they are already here.

anonymous · Answer

If we solve the given equation, and you got 1, then perhaps we're supposed to substitute the 1 in for x in the equation we created, which would allow us to solve for y.  Right?

phi · Answer

This question has been asked before.
I'll look for the post.

anonymous · Answer

Ok

anonymous · Answer

Thank you!

phi · Answer

http://openstudy.com/study#/updates/5372fefbe4b0c1175e755dc4 ganesh posted a graph showing the two possible solutions.

phi · Answer

The constraint
bullfrog can not eat more than seven flies in one week.

probably means  the frog can eat 7 flies on the first day (and none after that for a week),  or  1 per day, or any combination , as long as it's less than 7 for that week.

the plot shows x in days.
to show the constraint, plot the line y= 7.  No solution (in the first week, i.e. x<8)  is allowed to be above 7

anonymous · Answer

I think I understand...based on the problem, I'm supposed to finding the values for x, correct?

phi · Answer

we solve the problem by finding where the two curves intersect, and then check that these points meet the constraint.  We find two possible solutions
(3,8)   eat 8 flies on the 3rd day   or
(1,2)   eat 2 flies on the first day

only the second meets the constraint of 7 or fewer flies can be eaten in the first week.

anonymous · Answer

That makes so much more sense.  Thank you for explaining it to me!

phi · Answer

yes.

She has devised an equation to solve for which day (x) 

so you find x.  you also find the corresponding y (to make sure we meet the constraint i.e.  y value is less than 7 )

anonymous · Answer

Thank you so much for the help!!

phi · Answer

yw