Question
The Coleman family purchased a camper van for $38,000. The van is predicted to depreciate by about 15% each year. Write an exponential equation in the form y=a(b)x that can model the value of the van, y, in x years. Use whole numbers, decimals, or simplified fractions for the values of a and b. y =
Answers
GPT-4o mini
To model the depreciation of the camper van, we can use the exponential decay formula in the form \( y = a(b)^x \), where:
- \( a \) is the initial value of the van,
- \( b \) is the decay factor,
- \( x \) is the number of years,
- \( y \) is the value of the van after \( x \) years.
1. The initial value \( a \) of the camper van is $38,000.
2. If the van is predicted to depreciate by about 15% each year, this means that it retains 85% of its value each year. To find the decay factor \( b \):
\[
b = 1 - \text{depreciation rate} = 1 - 0.15 = 0.85
\]
Now we can write the equation:
\[
y = 38000(0.85)^x
\]
So, the exponential equation that models the value of the camper van over time is:
\[
y = 38000(0.85)^x
\]
- \( a \) is the initial value of the van,
- \( b \) is the decay factor,
- \( x \) is the number of years,
- \( y \) is the value of the van after \( x \) years.
1. The initial value \( a \) of the camper van is $38,000.
2. If the van is predicted to depreciate by about 15% each year, this means that it retains 85% of its value each year. To find the decay factor \( b \):
\[
b = 1 - \text{depreciation rate} = 1 - 0.15 = 0.85
\]
Now we can write the equation:
\[
y = 38000(0.85)^x
\]
So, the exponential equation that models the value of the camper van over time is:
\[
y = 38000(0.85)^x
\]