Question

the following table gives information about new hotel construction in a certain country from the fourth - quarter of 2007 through the first quarter of 2009.

yearly quarter	2007 q4	2008 q1	2008 q2	2008 q3	2008 q4	2009 q1
number of new hotel projects, h	438	449	381	403	388	379

answer parts a through e.

a. plot the data points using ordered pairs of the form (t,h). choose the correct graph below.

b. determine the average rate of change of new hotel construction projects from 2007 q4 to 2008 q1.
21 new hotels/quarter
c. determine the average rate of change of new hotel construction projects from 2008 q3 to 2009 q1.
blank new hotels/quarter

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 $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x$ represents the number of quarters since 2007 Q4 and $h$ represents the number of new hotel projects.

Step2: Identify values for 2008 Q3 and 2009 Q1

For 2008 Q3, $x_1 = 3$ and $h_1=403$. For 2009 Q1, $x_2 = 5$ and $h_2 = 279$.

Step3: Calculate the average rate of change

Substitute the values into the formula: $\frac{h_2 - h_1}{x_2 - x_1}=\frac{279 - 403}{5 - 3}=\frac{- 124}{2}=-62$.

Answer:

-62 new hotels/quarter