Question

The following function represents the value of a house, in dollars, after x years:

f(x) = 242,000(1.04)x

What does 1.04 represent?
The present value of the house
The value of the house after x years
The increase in the value of the house per year, which is 4%
The value of the house after x years, which will be 4% of the present value

Answer 1

the 1.04 represents the increase in the house value each year, which is 4%

Answer 2

The correct option is 3.

Explanation:

The general exponential growth model is

`y=a(1+r)^x` .... (1)

where, a is the initial value, r is growth rate per period and x is number of periods. Here (1+r) is growth factor.

The given function is

`f(x)=242,000(1.04)^x`

It can be written as

`f(x)=242,000(1+0.04)^x` .... (2)

From (1) and (2) we get

`r=0.04=4\%`

In the given function 1.04 is growth factor. It means it represents increase in the value of the house per year which is 4%.

Therefore the correct option is 3.