Answer:
Therefore, the correct answer is option C. 21 tickets per hour.
Step-by-step explanation:
Given: the opening day ticket sales for the park is given by the function[tex]T(h)=\frac{386+110h}{h}[/tex] where [tex]T(h)[/tex] represents the number of tickets sold [tex]h[/tex] hours after opening at 7:00 a.m.
To find: the rate of change in the number of tickets sold between 10:00 a.m and 1:00 p.m.
For 10 a.m., [tex]h=3[/tex]
So the number of tickets sold upto 10 a.m. are,
[tex]T(3)=\frac{386+110 (3)}{3}[/tex]
[tex]T(3)=238.67[/tex]
Similarly, for 1 p.m., [tex]h=6[/tex] hours
So, the number of tickets sold in 6 hours are,
[tex]T(6)=\frac{386+110(6)}{6}[/tex]
[tex]T(6)=174.33[/tex]
Now, the rate of change in the number of tickets sold between 10:00 a.m and 1:00 p.m is,
[tex]\frac{T(6)-T(3)}{6-3}[/tex]
[tex]=\frac{174.33-238.67}{3}[/tex]
[tex]=-21.445[/tex]
which is approximately [tex]-21[/tex] tickets per hour.
Hence, the rate of change in the number of tickets sold between 10:00 a.m and 1:00 p.m is -21 tickets per hour.
The correct answer is option C.
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