the following table gives information about new hotel construction in a certain country from the fourth…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. In the context of the hotel - construction problem, if $h(t)$ is the number of new hotel projects as a function of the number of quarters $t$ since 2007 Q4, the average rate of change over the interval $[t_1,t_2]$ is $\frac{h(t_2)-h(t_1)}{t_2 - t_1}$.

Step2: Calculate average rate of change from 2007 Q4 to 2008 Q1

For 2007 Q4, $t_1 = 0$ and $h(t_1)=438$. For 2008 Q1, $t_2 = 1$ and $h(t_2)=459$. Then the average rate of change is $\frac{h(1)-h(0)}{1 - 0}=\frac{459 - 438}{1}=21$ new hotels/quarter.

Step3: Calculate average rate of change from 2008 Q3 to 2009 Q1

For 2008 Q3, $t_1 = 3$ and $h(t_1)=403$. For 2009 Q1, $t_2 = 5$ and $h(t_2)=279$. Then the average rate of change is $\frac{h(5)-h(3)}{5 - 3}=\frac{279 - 403}{2}=\frac{- 124}{2}=-62$ new hotels/quarter. The negative sign indicates a decrease in the number of new hotel projects.

Answer:

b. 21 new hotels/quarter c. - 62 new hotels/quarter