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.\n\n| yearly quarter | 2007 q4 | 2008 q1 | 2008 q2 | 2008 q3 | 2008 q4 | 2009 q1 |\n|--|--|--|--|--|--|--| \n| quarters since 2007 q4, t | 0 | 1 | 2 | 3 | 4 | 5 |\n| number of new hotel projects, h | 438 | 449 | 381 | 403 | 388 | 379 |\n\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.\n21 new hotels/quarter\nc. determine the average rate of change of new hotel construction projects from 2008 q3 to 2009 q1.\nblank new 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, $x$ 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