# How can functions be used to solve real-world situations?

##### 1 Answer

I'm going to use a few examples.

**The population of Wyoming at the end of 2014 was #584,513#. The population increases at an annual rate of #0.2%#.**

a) Determine an equation for the population with respect to the number of years after

*Solution*

The function will be of the form

b) Using this model, estimate the population of Wyoming in

*solution*

Here,

c) Using this model, determine in how many years it will take for the population to exceed

*Solution*

Here,

It will take

**A vending machine currently sells packages of chips that sell for $2.00 and they sell 100 packages. They find that for each 25 cent increase, they lose five customers. **

a) Write a function, in standard form, to represent this problem. Make sure that the dependant variable is "Profit".

*Solution*

We can use the following formula:

b) Determine the profit after

*Solution*

Here,

Hence, the profit after

c) Find the optimum price for the chips to maximize the profit for the company.

*Solution*

This will be the vertex of the function. We will need to complete the square.

The optimum price is

Hopefully this proves that functions can effectively model real world problems, and can be used to solve them!

Hopefully this helps!