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? more tickets were sold on the fourth day than on the 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. the same number of tickets was sold on the fourth day and 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 given by $\frac{T(b)-T(a)}{b - a}$. 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, $T(10)=T(4)$.

Answer:

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