Answer:
A) both functions are linear
B) f(x) = 7446.4x + 178713.6 and f(x) = 11000x + 179000
C) House 2 will value $106894.4 more than house 1.
Step-by-step explanation:
A) Value Increase from year 1 to year 2:
House 1: 193,606.40 - 186,160 = 7446.4
House 2: 201,000 - 190,000 = 11000
Value Increase from year 2 to year 3:
House 1: 201,350.66 - 193,606.40 = 7744.26
House 2: 212,000 - 201,000 = 11000
This means that a constant increament in x variable gives a constant increament in both houses vales. Then, both functions are linear.
B) The slope is the same as the value increment from one year to the next one.
slope (m) of House 1: 7446.4
slope (m) of House 2: 11000
General formula of a line:
f(x) = mx+b
Replacing with a known point:
<u>House 1</u>
186,160 = 7446.4(1) + b
b = 186,160 - 7446.4 = 178713.6
equation: f(x) = 7446.4x + 178713.6
<u>House 2</u>
190,000 = 11000(1) + b
b = 190,000 - 11000 = 179000
equation: f(x) = 11000x + 179000
C) Replacing x = 30 into each equaiton:
<u>Value of House 1 after 30 years</u>
f(x) = 7446.4(30) + 178713.6 = 402105.6
<u>Value of House 2 after 30 years</u>
f(30) = 11000(30) + 179000 = 509000
Then, house 2 will value 509000 - 402105.6 = $106894.4 more than house 1.
