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?

Options :

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

b. No tickets were sold on the fourth day and tenth day.

c. Fewer tickets were sold on the fourth day than on the tenth day.

d. More tickets were sold on the fourth day than on the tenth day.

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

Step-by-step explanation:

Given that the average rate of change in T(d), a function used to relate the number of tickets sold for a movie to the number of days since its release is 0 for interval: d=4 and d=10.

Rate of change measures the change in quantity in relation to another, in the scenario it could be interpreted as, the change in quantity of ticket t sold with respect to change in the number of days since the movies was released.

Therefore, if the average rate of change obtained for d =4 and d = 10 gives 0, then it could be inferred that the value of T(d) on both days are the same.

[T(10) - T(4)] / 2 = 0

Then T(10) = T(4)

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