the following table shows the monthly rent of a one - bedroom apartment in a city in certain years.\n\n(a)…

the following table shows the monthly rent of a one - bedroom apartment in a city in certain years.\n\n(a) find the the average rate of change of the monthly rent from 2007 to 2011.\n$ per year\n\n(b) find the average rate of change of the monthly rent from 2011 to 2019.\n$ per year

the following table shows the monthly rent of a one - bedroom apartment in a city in certain years.\n\n(a) find the the average rate of change of the monthly rent from 2007 to 2011.\n$ per year\n\n(b) find the average rate of change of the monthly rent from 2011 to 2019.\n$ per year

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for 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 year and (y) represents the rent.

Step2: Calculate for part (a)

For the interval from (2007) ((x_1 = 2007)) to (2011) ((x_2=2011)), (f(x_1)=825), (f(x_2) = 955). The change in (x) is (x_2 - x_1=2011 - 2007=4). The change in (y) is (f(x_2)-f(x_1)=955 - 825 = 130). The average rate of change is (\frac{955 - 825}{2011 - 2007}=\frac{130}{4}=32.5).

Step3: Calculate for part (b)

For the interval from (2011) ((x_1 = 2011)) to (2019) ((x_2=2019)), (f(x_1)=955), (f(x_2)=1275). The change in (x) is (x_2 - x_1=2019 - 2011 = 8). The change in (y) is (f(x_2)-f(x_1)=1275 - 955=320). The average rate of change is (\frac{1275 - 955}{2019 - 2011}=\frac{320}{8}=40).

Answer:

(a) (32.5) (b) (40)