For tax​ purposes, a business depreciates its ​$240 comma 000 building using​ "straight-line depreciation" over 12 years by reducing its value by ​1/12 of its original value each year. If we assume that the value of the building can be found or estimated at any point of time during this​ period, the value of the building can be modeled by the function yequals240 comma 000minus20 comma 000​x, where x is the number of years. Complete parts ​(a) through ​(c).

Question

What is the meaning of the​ y-intercept? Select the correct choice below and fill in the answer box to complete your choice.
​(Type an integer or a​ decimal.)
A.
The value of the building increases by ​$
  
enter your response here per year.
B.
The value of the building decreases by ​$
  
enter your response here per year.
C.
At the end of the 12 ​years, the building is worth ​$
  
enter your response here.
D.
At the beginning of the 12 ​years, the building is worth ​$
  
enter your response here.

Answer 1

To understand the meaning of the y-intercept in the function \( y = 240,000 - 20,000x \), we first need to recognize that in this context, the y-intercept represents the value of the building when \( x = 0 \).

When \( x = 0 \): \[ y = 240,000 - 20,000(0) = 240,000 \]

Thus, at the beginning of the 12 years (when \( x = 0 \)), the value of the building is $240,000.

Now let’s consider the answer options:

A. The value of the building increases by $___ per year.

B. The value of the building decreases by $___ per year.

C. At the end of the 12 years, the building is worth $___.

D. At the beginning of the 12 years, the building is worth $___.

Since we found that the value at the beginning of the 12 years (when \( x = 0 \)) is $240,000, the correct choice is:

D. At the beginning of the 12 years, the building is worth 240,000.