the following table gives information about new hotel construction in a certain country from the fourth…
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.\nyearly quarter 2007 q4 2008 q1 2008 q2 2008 q3 2008 q4 2009 q1\nquarters since 2007 q4, t 0 1 2 3 4 5\nnumber of new hotel projects, h 430 459 301 403 288 259\nanswer parts a through e\n\na. plot the data points using ordered pairs of the form (t,h). choose the correct graph below.\n\nb. determine the average rate of change of new hotel construction projects from 2007 q4 to 2008 q1\nnew hotels/quarter
Answer
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, $x$ is the number of quarters since 2007 Q4 ($t$) and $y$ is the number of new hotel projects ($h$). For the interval from 2007 Q4 ($t_1 = 0$) to 2008 Q1 ($t_2=1$), $h_1 = 430$ and $h_2 = 459$.
Step2: Calculate the average rate of change
The average rate of change $=\frac{h_2 - h_1}{t_2 - t_1}=\frac{459 - 430}{1-0}$. $=\frac{29}{1}=29$.
Answer:
29 new hotels/quarter