A certain calling card costs 5.2 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 52 cent connection fee. If is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent.
A) $0
B) $0.45
C) $0.57
D) $0.44
E) does not exist

Question

A certain calling card costs 5.2 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 52 cent connection fee. If  is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. ​  ​
A) $0 
B) $0.45 
C) $0.57 
D) $0.44 
E) does not exist

Quizplus · Accepted Answer

To create a table of charges for calls lasting close to 1 minute, we can round up the 5.2 cents per minute charge to 6 cents per minute. Then, for a call lasting t minutes:

- The cost of the call would be 6t cents
- Adding the 52 cent connection fee, the total cost would be 6t + 52 cents

Using t = 1 as a close approximation for a call lasting close to 1 minute, we get:

- The cost of the call would be 6 cents
- Adding the 52 cent connection fee, the total cost would be 58 cents

Taking the limit as t approaches 0, we get:

lim (t->0) (6t + 52) = 52

Therefore, the limit exists and is equal to 52 cents. Rounding to the nearest cent, we get 0.57, so the best choice is C, $0.57.

A Certain Calling Card Costs 5