Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation

Given that they want to estimate the cost of the house after 8 years, the best equation will be obtained as follows:

FV=P (1+r) ^n

where:

n=time

p=principle

r=rate

First we need to estimate the rate. The value of the house after 5 years is $ 190,000

thus plugging the values in the equation and solving for r we get:

190000=157200 (1+r) ^5

1.20865 = (1+r) ^5

getting the fifth root of both sides we obtain:

1.0386=1+r

thus

r=0.0386~3.86%

thus the value of the house after 8 years will be:

FV=157200 (1.0386) ^8

FV=$212,879.6936