Problem 73 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used an exponential model with a positive growth rate to describe the depreciation in my car's value over four years.

Step-by-Step Solution

Answer

No, it doesn't make sense to use an exponential model with a positive growth rate to describe the depreciation in a car's value. Car value depreciates or decreases over time, while positive exponential growth would indicate increasing values.

Step 1 - Understanding car value depreciation

First, let's understand 'Car depreciation'. It is the rate at which a car loses its value over time. Typically, a car's value decreases over time, not increases. So, depreciation refers to a declining value.

Step 2 - Understanding exponential growth model

Secondly, the 'Exponential model with a positive growth rate', is used for a quantity that increases over time. The quantity grows at a rate proportional to its current value, implying it gets larger as time progresses.

Step 3 - Analyzing the relation between car depreciation and exponential growth model

Upon analyzing, it is seen that the value of a car depreciates (decreases) over time, whereas an exponential model with positive growth rate implies the quantity will increase over time. Hence, using an exponential model with a positive growth rate to describe depreciation in a car’s value does not make sense as it contradicts the fundamental nature of depreciation and exponential growth.