Question

Due to crime rates in a certain city, home values began to decrease by 4% each year. If a home was purchased in 2015 for $315,000, write and use an exponential function to determine the amount the house will be worth in 2020. Round to the nearest whole dollar.

Answer 1

.

Explanation:

Answer 2

`A(t)=315000(0.96)^t\\A(5)=\$256842`

Explanation:

The exponential function for depreciation is given as:

`A(t)=A_o(1-r)^t` where:

`A_o$ is the initial value\\r is the depreciation rate\\t is the number of time period (in years) after the initial point`

In the case of the home:

`A_o=$315,000\\r=4\%=0.04`

Therefore, the exponential function modeling the depreciation of the home's value is:

`A(t)=315000(1-0.04)^t\\A(t)=315000(0.96)^t\\`

We want to determine the worth of the home in 2020.

t=2020-2015=5 years

Therefore:

`A(5)=315000(0.96)^5\\A(5)=\$256842.40`

The home is worth $256,842 in the year 2020.