Question

12 2,110
18 1,500
24 870
30 220
she calculates two regression models. which is true?
the linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.
the linear model better represents the situation because according to the exponential model, the repayment amount will never be 0.
the exponential model better represents the situation because the amount she owes decreases by about the same amount every 6 months.
the exponential model better represents the situation because according to the linear model, the repayment amount will eventually be negative.

Explanation:

1. Analyze the linear model issue: A linear model for debt repayment might predict a negative amount (since debt can't be negative), which is unrealistic.
2. Analyze the exponential model: The graph and table show a decreasing curve, typical of exponential decay (amount decreases by a percentage, not fixed amount). Also, exponential models approach zero but don't reach it, but the key issue with linear is negative values.
3. Evaluate options:

• First option: Amount doesn't decrease by same amount (e.g., 2110 - 1500 = 610; 1500 - 870 = 630; 870 - 220 = 650 – not same, so linear is wrong).
• Second option: Exponential never being zero isn't a reason to pick linear (debt can be paid off, but linear's negative issue is worse).
• Third option: Amount doesn't decrease by same amount (so exponential's "same amount" claim is wrong).
• Fourth option: Linear model would eventually have negative debt (impossible), so exponential (which decays, not becoming negative) is better.

Answer:

D. The exponential model better represents the situation because according to the linear model, the repayment amount will eventually be negative.