Question

5.

Nicki just bought a house priced at $245,000. If home prices are increasing by 3.5% each year:
a) Write an equation that will calculate the value of her house in future years.
b) What will Nicki's house be worth in 4 years?

Answer 1

a)
`C(t)=245,000\cdot(1.035)^t`

b) Nicki's house is worth $281,143 in 4 years

Explanation:

Exponential Growth Function

The exponential function is commonly used to model natural growing or decaying processes where the change is proportional to the actual quantity.

An exponential growth function is expressed as:

`C(t)=C_o\cdot(1+r)^t`

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the growth positive rate, expressed in decimal

Nicki paid Co=$245,000 for a house and it's known that home prices increase by r=3.5%=0.035 each year.

a)

Substituting the given values, the equation is:

`C(t)=245,000\cdot(1+0.035)^t`

`\mathbf{C(t)=245,000\cdot(1.035)^t}`

b) The value of Nicki's house in t=4 years is:

`C(4)=245,000\cdot(1.035)^4`

`C(4)=245,000\cdot 1.148=281,143`

Nicki's house is worth $281,143 in 4 years