maria created a graph of $b(t)$, the temperature over time. for the interval between $t = 3$ and $t = 7$…

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 $t = 3$.

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 $t = 3$.

Answer

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $B(t)$ over $[a,b]$ is $\frac{B(b)-B(a)}{b-a}$.

Step2: Plug in given values

Here, $a=3$, $b=7$, average rate $=8$. So: $$8 = \frac{B(7)-B(3)}{7-3}$$

Step3: Solve for $B(7)-B(3)$

Simplify denominator: $7-3=4$. Multiply both sides by 4: $$B(7)-B(3)=8\times4=32$$

Answer:

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