Mary Ann pays a monthly fee for her cell phone package which includes 700 minutes. She gets Billed an additional charge for every minute she uses the phone past the 700 minutes. During her first month, Mary Ann used 26 additional minutes and her bill was $37.79. During her second month, Mary Ann used 38 additional minutes and her bill was $41.39. i. Write a function that represents the total monthly cost C(x) of Mary Ann’s cell phone package, where x is the number of additional minutes used. ii. Find the inverse function iii. What do x and C-1(x) represent in the context of the inverse function? iv. How many additional minutes did Mary Ann use if her bill for her third month was $48.89?

Solution.

1. Let be x is the number of additional minutes used and y is monthly fee for Mary Ann's cell phone package which includes 700 minutes. Then$26x+y=37.79,\newline 38x+y=41.39.$

From here one additional minute costs $x=0.3 \$$ and monthly fee is $y=29.99\$.$

So, function that represents the total monthly cost C(x) of Mary Ann’s cell phone package is

$C(x)=29.99+0.3x$

2.

Find the inverse function:

$0.3x=C(x)-29.99,$

$x=\frac{10}{3}C(x)-\frac{299.9}{3}.$

Therefore,

$C^{-1}(x)=\frac{1}{3}(10x-299.9)$

3.

$C^{-1}(x)$ represents a number of additional minutes,

x represents Mary Ann's monthly total phone cost.

4.

Use formula $C^{-1}(x)=\frac{1}{3}(10x-299.9).$

Then

$C^{-1}(48.89)=\frac{1}{3}(10•48.89-299.9)=63$additional minutes.