Question

A new apartment building was bought for $175,000 9 years ago. The owners calculated that the building appreciated $3,000 per year. Find an explicit formula that describes the appreciation of the building, if x is the number of years since the purchase.

Answer 1

The explicit formula to describe the appreciation of the building is V(x) = $175,000 + ($3,000 × x), where V(x) is the value of the apartment after x years, $175,000 is the initial value, and $3,000 is the yearly rate of appreciation.

Step-by-step explanation:

The student is asking for an explicit formula that describes the appreciation of an apartment building over time, given that it appreciates at a constant rate. The initial value of the building is $175,000 and it appreciates at a rate of $3,000 per year.

Step-by-Step Appreciation Calculation

To find the value of the apartment building after x years, we can use the formula for simple appreciation, which is:

V(x) = V0 + (rate of appreciation) × x

Where:
V(x) = Value of the apartment after x years
V0 = Initial value of the apartment building
rate of appreciation = $3,000 per year

Substituting the given values, we get:

V(x) = $175,000 + ($3,000 × x)

This is the explicit formula which can be used to calculate the value of the apartment after any number of years x.