Question

A travel trailer bought today will depreciate over time at a fairly steady rate, as shown in the table.



Years Value ($)
0 40,000
1 34,000
2 29,000
3 24,500
4 21,000
5 17,500




Using a function fit to this data, which dollar amount would predict the trailer’s value in 10 years?


$3,500


$5,700


$7,900


$9,300

Answer 1

"Fairly steady rate" suggests a steady percentage (exponential) decay. Over 5 years the factor is 17,500/40,000 = 0.4375, so in 10 years the factor is 0.4375^2 = 0.19140625. Multiply by 40,000: 40,000·0.19140625 = 7,656.25 ≈ $7,900.

Answer: $7,900