# How to write quadratic function given the following information?

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An apartment complex has 1600 units available of which 800 are currently rented for 300 dollars per month. A market survey indicated that a each five dollar decrease in monthly rent will result in 20 new renters.

Write a function that models the monthly income, where x is the number of five dollar decreases in monthly rent. Then find the rent which yields the maximum monthly income, and what that income is.

An apartment complex has 1600 units available of which 800 are currently rented for 300 dollars per month. A market survey indicated that a each five dollar decrease in monthly rent will result in 20 new renters.

Write a function that models the monthly income, where x is the number of five dollar decreases in monthly rent. Then find the rent which yields the maximum monthly income, and what that income is.

##### 1 Answer

#### Explanation:

Well first off, you have to figure out how to write all of the terms in terms of

This part is pretty straightforward. The rent is going to start at

as the rent with each decrease. This is because you start at

So now, we have to find out how many renters we have at a given time. So the function is going to be your current renters, plus the amount of new renters you will get. Since the original

However, you will get new

Now, finally, from logic, we know that the amount of renters at a given time

So your final function is

(I just multiplied it out for the answer above, but you can check my work on that). Yay!