she calculates two regression models. which is true? the linear model better represents the situation…

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.

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.

Answer

Explanation:

Step1: Analyze linear - model property

In a linear model, if the relationship is $y = mx + b$, as $x$ (time in months here) increases, $y$ (amount owed) will keep decreasing at a constant rate. Eventually, if $m<0$, $y$ will become negative which is not possible in the context of the amount of debt owed.

Step2: Analyze exponential - model property

In an exponential decay model $y = a\cdot b^x$ ($0 < b<1$), $y$ will approach 0 but never reach it as $x$ increases. This is a more realistic model for debt - repayment where the amount owed decreases over time but never actually reaches 0 in a theoretical infinite time frame. Also, looking at the data points and the curve shape, the decrease is not a constant amount every 6 months (which would be characteristic of a linear model), but rather a percentage - based decrease which is typical of an exponential model.

Answer:

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