A certain calling card costs 6.8 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 68 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)$0.68
C)$0.75
D)$0.82
E)does not exist

Question

A certain calling card costs 6.8 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 68 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)$0.68 
C)$0.75 
D)$0.82 
E)does not exist

Quizplus · Accepted Answer

To create a table of charges for calls lasting close to 1 minute, we need to consider the charges for calls lasting between 0.5 and 1.5 minutes (rounded up to the nearest minute).
For a call lasting 0.5 minutes, the charge would be 7.48 cents (rounded up from 6.8 cents) + 68 cents connection fee = 75.48 cents.
For a call lasting 1.5 minutes, the charge would be 14.18 cents (rounded up from 13.6 cents) + 68 cents connection fee = 82.18 cents.
Using these values, we can create a table of charges:
| Minutes | Charge |
|---------|---------|
| 0.5     | 75.48   |
| 1       | 75.68   |
| 1.5     | 82.18   |
Taking the limit as t approaches 1, we see that the charge approaches 75.68 cents, which is option C to the nearest cent.

A Certain Calling Card Costs 6