Question

t(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released. the average rate of change in t(d) for the interval d = 4 and d = 10 is 0. which statement must be true? the same number of tickets was sold on the fourth day and tenth day. no tickets were sold on the fourth day and tenth day. fewer tickets were sold on the fourth day than on the tenth day. more tickets were sold on the fourth day than on the tenth day.

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $y = T(d)$ over the interval $[a,b]$ is $\frac{T(b)-T(a)}{b - a}$. Here $a = 4$, $b=10$, and the average rate of change $\frac{T(10)-T(4)}{10 - 4}=0$.

Step2: Solve the equation

Since $\frac{T(10)-T(4)}{6}=0$, then $T(10)-T(4)=0\times6 = 0$. So $T(10)=T(4)$. This means the number of tickets sold on the fourth day is the same as the number of tickets sold on the tenth day.

Answer:

The same number of tickets was sold on the fourth day and tenth day.