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?\no the temperature was 8 degrees higher when $t = 7$ than when $t = 3$.\no the temperature was 8 times higher when $t = 7$ than when $t = 3$.\no the temperature was 32 degrees higher when $t = 7$ than when $t = 3$.\no 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?\no the temperature was 8 degrees higher when $t = 7$ than when $t = 3$.\no the temperature was 8 times higher when $t = 7$ than when $t = 3$.\no the temperature was 32 degrees higher when $t = 7$ than when $t = 3$.\no the temperature was 2 degrees higher when $t = 7$ than when $t = 3$.

Answer

Answer:

The temperature was 32 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)).

Step3: Calculate the value of (B(7)-B(3))

(8\times(7 - 3)=8\times4=32). This means the temperature at (t = 7) is 32 degrees higher than the temperature at (t = 3).