Question

For 12 months, Jeanne has belonged to a book-of-the-month club. Jeanne has spent $70.45 on the club. The first month, she paid the monthly fee and spent an additional $10.45 on books. She has only paid the monthly fee since then. What are the initial value and the rate of change of this function?

Answer 1

The initial value is $10.45

The rate of change is
`m=5\ \$/month`

Explanation:

Let

m-----> the the monthly fee

we know that

`12m+10.45=70.45`

Solve for m

`12m=70.45-10.45`

`12m=60`

`m=5\ \$/month`

Find the linear equation that represent this problem

Let

x -----> the number of months

y-----> amount Jeanne has spent monthly

The equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope (the monthly fee)

`m=5\ \$/month`

so

`y=5x+b`

Remember that

The first month, she paid the monthly fee and spent an additional $10.45

For x=1, y=5+10.45=15.45

substitute

`15.45=5(1)+b`

`b=15.45-5=10.45`

The equation is

`y=5x+10.45`

therefore

The initial value is $10.45

The rate of change is the slope of the linear function
`m=5\ \$/month`