6. the average rate of change of p(t) between t = 0 and t = b is 50. find b. m b = 4 p b = 8 r b = 10 s b = 50

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = P(t)$ from $t = a$ to $t = b$ is $\frac{P(b)-P(a)}{b - a}$. Here, $a = 0$, $P(0)=100$, $P(b) = 500$, and the average rate of change is 50. So, $\frac{P(b)-P(0)}{b - 0}=50$.

Step2: Substitute the values

Substitute $P(0)=100$ and $P(b)=500$ into the formula: $\frac{500 - 100}{b}=50$.

Step3: Simplify the numerator

$500−100 = 400$, so the equation becomes $\frac{400}{b}=50$.

Step4: Solve for $b$

Cross - multiply: $50b=400$, then $b=\frac{400}{50}=8$.

Answer:

P. $b = 8$