To determine which statement must be true, we can analyze the change in temperature over the given time interval and the average rate of change in Maria's graph of [tex]\(B(t)\)[/tex].
Given data:
- The time interval is from [tex]\(t=3\)[/tex] to [tex]\(t=7\)[/tex], so [tex]\(t_1 = 3\)[/tex] and [tex]\(t_2 = 7\)[/tex].
- The average rate of change in the temperature over this interval is 8 degrees per unit of time.
First, calculate the length of the time interval:
[tex]\[
\Delta t = t_2 - t_1 = 7 - 3 = 4
\][/tex]
Next, use the average rate of change to determine the change in temperature ([tex]\(\Delta \text{Temp}\)[/tex]):
[tex]\[
\Delta \text{Temp} = (\text{Average Rate of Change}) \times (\Delta t) = 8 \times 4 = 32
\][/tex]
Thus, the temperature increased by 32 degrees from [tex]\(t=3\)[/tex] to [tex]\(t=7\)[/tex].
Given the result, the correct statement is:
"The temperature was 32 degrees higher when [tex]\(t=7\)[/tex] than when [tex]\(t=3\)[/tex]."
Therefore, the statement that must be true is:
"The temperature was 32 degrees higher when [tex]\(t=7\)[/tex] than when [tex]\(t=3\)[/tex]."
