To determine which statement is true, we need to analyze the given information about the average rate of change of the function [tex]\( T(d) \)[/tex], which denotes the number of tickets sold on day [tex]\( d \)[/tex].
The average rate of change of [tex]\( T(d) \)[/tex] over the interval from [tex]\( d = 4 \)[/tex] to [tex]\( d = 10 \)[/tex] is given as 0. The average rate of change of a function over an interval [tex]\([a, b]\)[/tex] can be calculated using the formula:
[tex]\[
\frac{T(b) - T(a)}{b - a}
\][/tex]
In this case:
[tex]\[
a = 4 \quad \text{and} \quad b = 10
\][/tex]
Thus, the average rate of change is:
[tex]\[
\frac{T(10) - T(4)}{10 - 4}
\][/tex]
Since we know that the average rate of change is 0, we can set up the following equation:
[tex]\[
\frac{T(10) - T(4)}{6} = 0
\][/tex]
To solve this equation, multiply both sides by 6 (the length of the interval):
[tex]\[
T(10) - T(4) = 0
\][/tex]
This simplifies to:
[tex]\[
T(10) = T(4)
\][/tex]
This means that the number of tickets sold on the tenth day, [tex]\( T(10) \)[/tex], is equal to the number of tickets sold on the fourth day, [tex]\( T(4) \)[/tex].
Therefore, the correct statement is:
"The same number of tickets was sold on the fourth day and tenth day."
