Question

The owners of an apartment building bought it new and then 2 years later sold it for $120000. They calculated that the building appreciated $10000 per year while they owned it.

Find a linear function that describes the value of the building over time, if
is the age of the apartment building.
V(x)=

Answer 1

The linear function that describes the value of the building over time is V(x) = $100,000 + $10,000x, where V(x) is the value of the building when it is x years old.

Step-by-step explanation:

To find a linear function that describes the value of the apartment building over time, we use the given information that the building appreciated $10,000 per year and sold for $120,000 after 2 years. Since the appreciation is linear, we can express the value V(x) as a function of the building's age x with an initial value V0 and a rate of change (slope) m. The linear function will be in the form V(x) = V0 + mx, where V0 is the initial value of the building and m is the rate of appreciation per year.

To determine V0, we know that after 2 years (when x=2), the building sold for $120,000. Thus, V(2) = V0 + 2m = $120,000. We also know that m = $10,000 per year, so we can write V0 + 2 ($10,000) = $120,000. Solving for V0, we find that the original value of the building was $100,000. Therefore, the linear function that models the building's value over time is V(x) = $100,000 + $10,000x.

Answer 2

The correct answer is V(x)= 100,000 +10,000x

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Price of the apartment after 2 years = US$ 120,000

Calculated appreciation of the apartment annually = US$ 10,000

2. Find a linear function that describes the value of the building over time, if x is the age of the apartment building.

V(x)= Original price of the apartment + Annual appreciation * Age of the apartment in years

Original price of the apartment = 120,000 - 2 * 10,000

Original price of the apartment = 120,000 - 20,000

Original price of the apartment = 100,000

Now, replacing with the values we know to build the linear function, we have:

V(x)= 100,000 +10,000x