Question

select the correct answer.
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 ( t ( h ) ) is the number of tickets sold ( h ) hours after opening at 7:00 a.m.
( t ( h ) = \frac { 386 + 110 h } { h } )
what is the approximate rate of change in the number of tickets sold between 10:00 a.m and 1:00 p.m?
a. -21 tickets per hour
b. -110 tickets per hour
c. -39 tickets per hour
d. -64 tickets per hour

Explanation:

Step1: Determine the time interval

From 7:00 a.m. to 10:00 a.m. is \(h_1 = 3\) hours, and from 7:00 a.m. to 1:00 p.m. is \(h_2=6\) hours.

Step2: Calculate the number of tickets at \(h = 3\) and \(h = 6\)

When \(h = 3\), \(T(3)=\frac{386+110\times3}{3}=\frac{386 + 330}{3}=\frac{716}{3}\approx238.67\)
When \(h = 6\), \(T(6)=\frac{386+110\times6}{6}=\frac{386+660}{6}=\frac{1046}{6}\approx174.33\)

Step3: Calculate the rate of change

The rate of change formula is \(\frac{T(h_2)-T(h_1)}{h_2 - h_1}\). Substitute \(h_1 = 3\), \(h_2=6\), \(T(3)\approx238.67\), \(T(6)\approx174.33\) into the formula: \(\frac{174.33 - 238.67}{6 - 3}=\frac{- 64.34}{3}\approx - 21\)

Answer:

A. -21 tickets per hour