Question

t(t) models the temperature (in degrees celsius) in windhoek, namibia when its t hours after midnight on a given day. when did the temperature increase faster? choose 1 answer: between 6 am and 9 am between 9 am and 1 pm the temperature increased at the same rate over both intervals

Explanation:

Step1: Calculate the rate of temperature increase between 6 am and 9 am

The formula for the average rate of change is \(\frac{T(t_2)-T(t_1)}{t_2 - t_1}\). Here, \(t_1 = 6\), \(T(t_1)=19\), \(t_2 = 9\), \(T(t_2)=25\).

$$ \frac{25 - 19}{9 - 6}=\frac{6}{3}=2 $$

Step2: Calculate the rate of temperature increase between 9 am and 1 pm

1 pm is \(t = 13\). Using the formula \(\frac{T(t_2)-T(t_1)}{t_2 - t_1}\), with \(t_1 = 9\), \(T(t_1)=25\), \(t_2 = 13\), \(T(t_2)=31\)

$$ \frac{31 - 25}{13 - 9}=\frac{6}{4}=1.5 $$

Answer:

A. Between 6 am and 9 am