To solve the problem, let's analyze the concept of the average rate of change and apply it to the context of the question.
The average rate of change of a function over an interval [tex]\([d_1, d_2]\)[/tex] can be calculated using the formula:
[tex]\[
\text{Average Rate of Change} = \frac{T(d_2) - T(d_1)}{d_2 - d_1}
\][/tex]
In this problem, we are given:
- [tex]\( d_1 = 4 \)[/tex]
- [tex]\( d_2 = 10 \)[/tex]
- The average rate of change over the interval [tex]\( d_1 = 4 \)[/tex] to [tex]\( d_2 = 10 \)[/tex] is 0.
Using the given formula:
[tex]\[
\frac{T(10) - T(4)}{10 - 4} = 0
\][/tex]
[tex]\[
\frac{T(10) - T(4)}{6} = 0
\][/tex]
For the fraction to be equal to zero, the numerator must be zero:
[tex]\[
T(10) - T(4) = 0
\][/tex]
[tex]\[
T(10) = T(4)
\][/tex]
This implies that the number of tickets sold on the tenth day is the same as the number of tickets sold on the fourth day.
Therefore, the correct statement that must be true is:
- The same number of tickets was sold on the fourth day and the tenth day.
