select the correct answer. a new amusement park presold discounted tickets for the opening day as well as…

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)=386 + 210h / 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. -64 tickets per hour b. -39 tickets per hour c. -110 tickets per hour d. -21 tickets per hour

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)=386 + 210h / 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. -64 tickets per hour b. -39 tickets per hour c. -110 tickets per hour d. -21 tickets per hour

Answer

Explanation:

Step1: Determine the values of h

10:00 a.m. is 3 hours after 7:00 a.m. ($h_1 = 3$), 1:00 p.m. is 6 hours after 7:00 a.m. ($h_2=6$).

Step2: Calculate $T(h_1)$ and $T(h_2)$

$T(3)=\frac{386 + 210\times3}{3}=\frac{386+630}{3}=\frac{1016}{3}\approx338.67$. $T(6)=\frac{386 + 210\times6}{6}=\frac{386 + 1260}{6}=\frac{1646}{6}\approx274.33$.

Step3: Calculate the rate of change

The rate of change formula is $\frac{T(h_2)-T(h_1)}{h_2 - h_1}$. $\frac{274.33 - 338.67}{6 - 3}=\frac{- 64.34}{3}\approx - 21.45\approx - 21$ tickets per hour.

Answer:

D. -21 tickets per hour