A ski rental shop charges $7.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $56.00 for all day. If equals the total charge for the ski equipment for t hours, determine the limit , if it exists.
A) $45.50
B) $42.00
C) $49.00
D) The limit does not exist.

Question

A ski rental shop charges $7.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $56.00 for all day. If  equals the total charge for the ski equipment for t hours, determine the limit  , if it exists.
A) $45.50 
B) $42.00 
C) $49.00 
D) The limit does not exist.

Quizplus · Accepted Answer

The total charge for t hours can be expressed as:

11eaa88b_944d_ab3c_a696_99f0321e335f_TB5869_11 = $7t, if $7t ≤ $56
11eaa88b_944d_ab3c_a696_99f0321e335f_TB5869_11 = $56, if $7t > $56

To find the limit, we need to consider what happens as t approaches infinity.

If t increases without bound, then the total charge will approach $56 because the shop will charge the maximum fee of $56 for all day.

Therefore, the limit of 11eaa88b_944d_ab3d_a696_6b61e8246de5_TB5869_11 as t approaches infinity is $56.

The answer choice closest to $56 is C) $49.00, so that is the best choice.

A Ski Rental Shop Charges $7