We have to find value of the house in 8 years so we will plug t=8 years in given equation.
[tex] y=150000(1.004)^{\left(12t\right)} [/tex]
[tex] y=150000(1.004)^{\left(12*8\right)} [/tex]
[tex] y=150000(1.004)^{96} [/tex]
[tex] y=150000(1.46702133432) [/tex]
[tex] y=220053.200148 [/tex]
Hence house will worth approx $220053.20 in 8 years.
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 y = 150000(1.004)12t How much will their house be worth in 8 years?
Solution:
Equation of the appreciation of the value of house is given by:-
[tex]y=150000(1.004)^{12t}[/tex]
We need to find the worth of the house after 8 years
So, that means time, t=8
Let us plug t=8 in the equation [tex]y=150000(1.004)^{12t}[/tex]
So, we get,
[tex]y=150000(1.004)^{12*(8)}[/tex]
[tex]y=150000(1.004)^{96}[/tex]
[tex]y=150000(1.467021)[/tex]
y=150000*1.467021
y=220053.20
In 8 years the value appreciates to $220053.20, that s, worth of house after 8 years=$22005320
