Brief Calculus.

Question

The credit remaining on a phone card ( in dollars) is a linear functions of the total calling time made with the card ( in minutes). The remaining credit after 27 minutes of calls is $16.83, and the remaining credit after 61 minutes of calls is $ 12.07.

a) Write a linear function relating the credit remaining on the phone card and the number of minutes used. clearly define your variable. Use function notation in your answer.

b) What is the slope? Write a sentence interpreting the meaning of the slope in this scenario. Don't forget the units.

Answer 1

a)

Let t be the time in minutes and B be the beginning credit and R be the remaining credit.

R(t) = B-mt

where m = the slope

We have two simultaneous equations.

16.83 = B-27m

12.07 = B-64m

Solving, m = 4.67/37, B ≈ 20.30

R(t) = 20.30-(4.67/37)t

b)

The slope is 4.67/37.

The slope is the number of credits per minute that is removed from the phone card. (dollars/minute)