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 2 degrees higher when t = 7 than when t = 3. the temperature was 32 degrees higher when t = 7 than when t = 3. 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.

Explanation:

Step1: Recall average rate - of - change formula

Average rate of change of $B(t)$ from $t = a$ to $t = b$ is $\frac{B(b)-B(a)}{b - a}$. Here $a = 3$, $b = 7$, and average rate is 8. So $\frac{B(7)-B(3)}{7 - 3}=8$.

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

$B(7)-B(3)=8\times(7 - 3)=32$.

Answer:

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