Question

maria created a graph of b(t), the temperature over time. for the interval between t = 3 and t = 7, the average rate of change in her graph of b(t) is 8. which statement must be true? the temperature was 8 degrees higher when t = 7 than when t = 3. the temperature was 8 times higher when t = 7 than when t = 3. the temperature was 32 degrees higher when t = 7 than when t = 3. the temperature was 2 degrees higher when t = 7 than when t = 3.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = B(t)$ over the interval $[a,b]$ is given by $\frac{B(b)-B(a)}{b - a}$. Here, $a = 3$, $b = 7$, and the average rate of change $\frac{B(7)-B(3)}{7 - 3}=8$.

Step2: Solve for $B(7)-B(3)$

Cross - multiply the equation $\frac{B(7)-B(3)}{7 - 3}=8$. Since $7-3 = 4$, we have $B(7)-B(3)=8\times(7 - 3)$.
$B(7)-B(3)=8\times4=32$. This means the temperature at $t = 7$ is 32 degrees higher than the temperature at $t = 3$.

Answer:

The temperature was 32 degrees higher when $t = 7$ than when $t = 3$.