A certain calling card costs 6.3 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 63 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)$0.56
C)$0.69
D)$0.78
E)does not exist

Question

A certain calling card costs 6.3 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 63 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)$0.56 
C)$0.69 
D)$0.78 
E)does not exist

Quizplus · Accepted Answer

To create the table for calls lasting close to 1 minute, we'll round up t to 1 and use the formula:

charge = (6.3 cents/minute) + 63 cents

charge = 69.3 cents

So for calls lasting close to 1 minute, the charge will be approximately 69 cents.

To find the limit as t approaches 0, we will use the formula:

lim as t->0+ [charge] = lim as t->0+ [(6.3t + 63)/100]

Evaluating this limit, we get:

lim as t->0+ [(6.3t + 63)/100] = 63/100 = 0.63

Rounding this to the nearest cent, we get $0.69 as the answer, which is choice C.

A Certain Calling Card Costs 6