Question

1. the number of people, p, at a playground after t min is given by $p = t^3 + 4t + 20$. the average rate of change of the number of people at the playground from 3 min to 4 min is ______

Explanation:

Step1: Calculate P(4)

Substitute $t=4$ into $P(t)=t^3+4t+20$
$P(4)=4^3 + 4(4) + 20 = 64 + 16 + 20 = 100$

Step2: Calculate P(3)

Substitute $t=3$ into $P(t)=t^3+4t+20$
$P(3)=3^3 + 4(3) + 20 = 27 + 12 + 20 = 59$

Step3: Compute average rate of change

Use formula $\frac{P(4)-P(3)}{4-3}$
$\frac{100 - 59}{4 - 3} = \frac{41}{1} = 41$

Answer:

41