Question

A new amusement park presold discounted tickets for the opening day as well as upon arrival at the park. the opening day ticket sales for the park, including presales, is represented by this function, where is the number of tickets sold h hours after opening at 7:00 a.m. what is the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m.? a. tickets per hour b. tickets per hour c. tickets per hour d. tickets per hour

Answer 1

The approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour

How to determine the rate of change?

The missing part of the question is represented by the following function:

$T(h) = \frac{386 + 110h}{h}$

10:00 a.m is 3 hours after 7:00 am and 1:00 p.m is 6 hours after 7:00 am.

This means that:

h = 3 at 10:00 am

h = 6 at 1:00 pm

Next, we calculate T(3) and T(6)

$T(3) = \frac{386 + 110*3}{3} =238.7$

$T(6) = \frac{386 + 110*6}{6} =174.3$

The average rate of change is then calculated as:

$T'(h) = \frac{T(3) - T(6)}{3 - 6}$

This gives

$T'(h) = \frac{238.7 - 174.3}{-3}$

Evaluate

T'(h) = -21

This means that the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour

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