To determine which statement is true, we need to understand the information given:
1. The interval between [tex]\( t=3 \)[/tex] and [tex]\( t=7 \)[/tex].
2. The average rate of change in the temperature graph [tex]\( B(t) \)[/tex] over that interval is 8 degrees per unit time.
The average rate of change is calculated using the formula for the average rate of change, which is:
[tex]\[
\text{Average Rate of Change} = \frac{\Delta B}{\Delta t}
\][/tex]
where [tex]\(\Delta B\)[/tex] is the change in temperature and [tex]\(\Delta t\)[/tex] is the change in time.
Here, the average rate of change is given as 8 degrees per unit time. We can rewrite it as:
[tex]\[
8 = \frac{\Delta B}{7 - 3}
\][/tex]
Since [tex]\( \Delta t = 7 - 3 = 4 \)[/tex]:
[tex]\[
8 = \frac{\Delta B}{4}
\][/tex]
To find the change in temperature ([tex]\(\Delta B\)[/tex]), we solve for [tex]\(\Delta B\)[/tex] by multiplying both sides of the equation by 4:
[tex]\[
\Delta B = 8 \times 4 = 32
\][/tex]
This calculation shows that the change in temperature between [tex]\( t=3 \)[/tex] and [tex]\( t=7 \)[/tex] is 32 degrees.
Therefore, the statement "The temperature was 32 degrees higher when [tex]\( t=7 \)[/tex] than when [tex]\( t=3 \)[/tex]" is the correct one.
