What is the remaining credit after 50 minutes of calls

Question

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 24 minutes of calls is $21.88, and the remaining credit after 38 minutes of calls is $20.06. What is the remaining credit after 50 minutes of calls?

Answer 1

c(t) = mt + b; m = (21.88 - 20.06)/(24 - 38) = - $0.13 per minute; c(t) = - 0.13t + b; 21.88 + 0.13·24 = b; b = 25;

c(t) = - 0.13t + 25; c(50) = - 0.13·50 + 25 = $18.50