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 the formula for average rate of change

The average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is given by \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). For the function \(T(d)\) over the interval \([4,10]\), the average rate of change is \(\frac{T(10)-T(4)}{10 - 4}\).

Step2: Analyze the given average rate of change

Since the average rate of change \(\frac{T(10)-T(4)}{10 - 4}=0\), then \(T(10)-T(4)=0\) (because \(10 - 4=6
eq0\)). By adding \(T(4)\) to both sides of the equation \(T(10)-T(4)=0\), we get \(T(10)=T(4)\).

Answer:

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