Question

Use the table to answer the question. The table lists the value of a car each year after it is purchased. Year 0 1 2 3 4 Value ($) 54,000 51,840 49,766 47,776 45,865 Determine whether the decreasing value can be modeled by a linear decay function or an exponential decay function, and why. (1 point) Responses exponential decay function; the value decreases by 4% per year, which is a constant percent rate of change exponential decay function; the value decreases by 4% per year, which is a constant percent rate of change exponential decay function; the value decreases by $6,000 per year, which is a constant percent rate of change exponential decay function; the value decreases by $6,000 per year, which is a constant percent rate of change linear decay function; the value decreases by 0.96 per year, which is a constant percent rate of change linear decay function; the value decreases by 0.96 per year, which is a constant percent rate of change linear decay function; the value decreases by 96% per year, which is a constant percent rate of change linear decay function; the value decreases by 96% per year, which is a constant percent rate of change

Answer 1

To determine whether the decreasing value of the car can be modeled by a linear decay function or an exponential decay function, we need to examine the changes in value each year.

Given the values:
- Year 0: $54,000
- Year 1: $51,840 (decrease of $2,160)
- Year 2: $49,766 (decrease of $2,074)
- Year 3: $47,776 (decrease of $1,990)
- Year 4: $45,865 (decrease of $1,911)

The difference in value each year is not constant, which suggests that it is not a linear function (which would have a constant amount subtracted each year).

Next, we can check the percentage decrease:
- From Year 0 to year 1: $51,840 is about 4% less than $54,000
- From Year 1 to year 2: $49,766 is about 4% less than $51,840
- From Year 2 to year 3: $47,776 is about 4% less than $49,766
- From Year 3 to year 4: $45,865 is about 4% less than $47,776

The value decreases by approximately the same percentage each year (about 4%), indicating that this value can be modeled by an exponential decay function.

The correct response is:
**Exponential decay function; the value decreases by 4% per year, which is a constant percent rate of change.**