To determine how much Harry pays back each month, we need to analyze the equation that models his remaining debt over time. The equation provided is:
[tex]\[ D = -200t + 9000 \][/tex]
Here's a step-by-step breakdown:
1. Understand the Components of the Equation:
- [tex]\( D \)[/tex] represents Harry's remaining debt in dollars.
- [tex]\( t \)[/tex] represents the number of months after he took out the loan.
- The term [tex]\( 9000 \)[/tex] represents the initial amount of the loan in dollars.
- The term [tex]\( -200t \)[/tex] represents the reduction in debt over time due to Harry's monthly payments.
2. Identify the Monthly Payment:
- The coefficient of [tex]\( t \)[/tex] in the term [tex]\(-200t\)[/tex] indicates the change in debt each month.
- A positive coefficient would indicate an increase in debt, while a negative coefficient indicates a decrease in debt.
- Here, the coefficient is [tex]\(-200\)[/tex], meaning Harry's debt decreases by [tex]$200 each month.
3. Interpret the Coefficient:
- The fact that the debt decreases by $[/tex]200 each month means that Harry pays back $200 each month.
Thus, the amount Harry pays back each month is:
[tex]\[ \boxed{200} \][/tex]
