Question

A home is purchased for $60,000 in 2001 and sold for $225,000 in 2021. Plot this on a graph. Then draw 2 lines, 1 mapping a linear relationship, and the other mapping an exponential one.
A. What is the average rate of change
B. Which model (linear or exponential) has a higher rate of change from 2010-2021?
C. What is the approximate value of the linear model in 2008?

Answer 1

Answer:

a. 3.6

b Linear

c. 2.13333

Plot a graph going up vertically by amounts 30,000  would be = 1

60,.000 would be = 2, 90,000 would be = 3 etc.

225,000 would show between 7 and 8. where marks of 15/30 = 1/2 would be counted back from 240,000 to 225,000 and between 210,000 to 240,000

After mapping the x rate must be 1 for both linear and for exponential.

The average rate of change is found when 60k = 2  and 225k = 7.5 is increasing and years shown 2001 to 2021 are shown on x axis.

=  20 years

Therefore linear shows 2 when x = 1 then shows 7.5 when x = 20

20/7.5 = 2.6

Therefore, this relationship is linear because each yyy-value is 7.5/20 more than the value before it. The x value goes up by 1 each value of 0.37 for y

When the value is exponential the y value should go up by 1 and as it is 30,000 each 1 value and x =1 goes up 2 2/3 = 2.6667 for every 30.000k to every x value.

A. 2 -2 2/3  = 2.31555.. average rate of change.for exponential  and between 3.5 and 3.7 = 3.6 average rate of change for linear.

B linear

C 2008 = 8 YEARS 8/20 X 2 = 0.8

0.8 X 2  2/3= 2.13333333 is the app value of the linear model 2008.