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