Question

p(t) models the number of people at the beach in rio de janeiro, brazil, when its t hours after midnight on a certain day.

when did the number of people increase faster?

choose 1 answer:

between 9 am and 10 am

between 10 am and 3 pm

the number of people increased at the same rate over both intervals

Explanation:

Step1: Calculate the rate of increase between 9 am and 10 am

The formula for the average rate of change is $\frac{\Delta P}{\Delta t}=\frac{P(t_2)-P(t_1)}{t_2 - t_1}$.
Here, $t_1 = 9$, $P(t_1)=28$, $t_2 = 10$, $P(t_2)=67$.
$\frac{P(10)-P(9)}{10 - 9}=\frac{67 - 28}{1}=39$ people per hour.

Step2: Calculate the rate of increase between 10 am and 3 pm

3 pm is \(t = 15\) (since \(t\) is hours after midnight).
$t_1 = 10$, $P(t_1)=67$, $t_2 = 15$, $P(t_2)=212$.
$\frac{P(15)-P(10)}{15 - 10}=\frac{212 - 67}{5}=\frac{145}{5}=29$ people per hour.

Answer:

A. Between 9 am and 10 am