College

The function [tex]f(t) = -5t + 150[/tex] models the amount of money, in millions of dollars, Hot PC Fix owes to banks, where [tex]t[/tex] is the number of years since 2000.

What is correct about the [tex]y[/tex]-intercept?

A. The [tex]y[/tex]-intercept is 150. It implies that the company owes 150 million dollars in 2000.
B. The [tex]y[/tex]-intercept is 5. It implies that the company pays back 5 million dollars per year.
C. The [tex]y[/tex]-intercept is -5. It implies that the company pays back 5 million dollars per year.
D. The [tex]y[/tex]-intercept is -150. It implies that the company owes 150 million dollars in 2000.

Answer :

To determine the correct information about the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(t) = -5t + 150 \)[/tex], let's analyze what the [tex]\( y \)[/tex]-intercept represents in this context.

1. Understanding the Function: The function [tex]\( f(t) = -5t + 150 \)[/tex] models the amount of money, in millions of dollars, that Hot PC Fix owes to banks. Here, [tex]\( t \)[/tex] is the number of years since 2000.

2. Identifying the [tex]\( y \)[/tex]-Intercept:
- The [tex]\( y \)[/tex]-intercept of a function is the point where the graph of the function crosses the [tex]\( y \)[/tex]-axis.
- This occurs when [tex]\( t = 0 \)[/tex].

3. Calculating the [tex]\( y \)[/tex]-Intercept:
- Substitute [tex]\( t = 0 \)[/tex] into the function:
[tex]\[
f(0) = -5(0) + 150 = 150
\][/tex]

4. Interpreting the [tex]\( y \)[/tex]-Intercept:
- When [tex]\( t = 0 \)[/tex], it corresponds to the year 2000.
- Therefore, the [tex]\( y \)[/tex]-intercept being [tex]\( 150 \)[/tex] means that in the year 2000, Hot PC Fix owed 150 million dollars to the banks.

5. Conclusion:
- The correct statement about the [tex]\( y \)[/tex]-intercept is: "The [tex]\( y \)[/tex]-intercept is 150. It implies that the company owes 150 million dollars in 2000."