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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?

Respuesta :

calculista

Answer:

The initial value is $10.45

The rate of change is  [tex]m=5\ \$/month[/tex]

Step-by-step explanation:

Let

m-----> the the monthly fee  

we know that

[tex]12m+10.45=70.45[/tex]

Solve for m

[tex]12m=70.45-10.45[/tex]

[tex]12m=60[/tex]

[tex]m=5\ \$/month[/tex]

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

[tex]y=mx+b[/tex]

where

m is the slope (the monthly fee)

[tex]m=5\ \$/month[/tex]

so

[tex]y=5x+b[/tex]

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

[tex]15.45=5(1)+b[/tex]

[tex]b=15.45-5=10.45[/tex]

The equation is

[tex]y=5x+10.45[/tex]

therefore

The initial value is $10.45

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

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