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Chapter 3: Problem 77

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.

Short Answer

Expert verified
Using an exponential model with a positive growth rate does not make sense to describe a car's depreciation, since the car鈥檚 value is decreasing over time rather than increasing. The correct model would be an exponential model with a negative growth rate as depreciation represents a decrease in value over time.

Step by step solution

01

Identifying the nature of depreciation

Car depreciation is the difference between how much a car is worth when you buy it and how much it's worth when you come to sell it or trade it in. Generally, a car's value tends to decrease over time due to factors such as age, mileage, wear and tear, market conditions etc. Thus, depreciation usually follows a negative growth rate.
02

Understanding an Exponential Model with a Positive Growth Rate

An exponential model will show the phenomenon of exponential growth. Specifically, an exponential model with a positive growth rate characterises consistent percent increase, which would mean that the entity in question is growing.
03

Assessing the compatibility of depreciation and exponential model with positive growth

Given that car depreciation represents a decrease in value and an exponential model with a positive growth rate signifies an increase in value, it does not make sense to use an exponential model with a positive growth rate to describe the depreciation in a car's value over time. The correct model for depreciation over time would rather be an exponential model with a negative growth rate.

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