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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."
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."
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