A 2 year old apartment building was sold for $155000. The owners calculated that the building appreciated $5000 per year while they owned it.
Find a linear function that describes the value of the building over time, if x is a number of years since the original purchase.
If its value grew by $5000/year for 2 years, then it was worth $10,000 more than it cost them. So, 2 years ago, it was worth $145,000. That means the value
v = 145,000 + 5000x
Function: V = Vo + 5000x.
V = Value over time.
Vo = Original value.
155,000 = Vo + 5000*2,
Vo = $145,000.
To find a linear function that describes the value of the building over time, we need to use the given information:
The original purchase price of the apartment building is $155,000, and the owners calculated that the building appreciated $5,000 per year while they owned it.
We know that the equation for a linear function is written in the form: y = mx + b, where:
- y represents the value of the building
- x represents the number of years since the original purchase
- m represents the slope or rate of change
- b represents the y-intercept or initial value
In this case, the slope represents the amount the building appreciates per year, which is $5,000. The y-intercept represents the original purchase price, which is $155,000.
So, the linear function that describes the value of the building over time can be written as:
y = $5,000x + $155,000