Question

A farmer buys a tractor for $10,000. If the tractor depreciates 10% per year, write an exponential decay function to fin the value of the tractor in 7 years.

Answer 1

F = P(1 - x)^n

F = 10,000(1 - 0.1)^7

F = 10,000(0.9)^7

F = $4,783

The value of the tractor in 7 years is $4,783

Explanation:

Applying the exponential depreciation equation;

F = P(1 - x)^n

Where;

F = final value after n years

P = initial value

x = depreciation rate (fraction)

n = time

Given;

P = $10,000

x = 10% = 0.10

n = 7 years

Substituting the given values;

F = 10,000(1 - 0.1)^7

F = 10,000(0.9)^7

F = 4782.969

F = $4,783

The value of the tractor in 7 years is $4,783