a machine that originally cost $15,600 has a value of $7,500 at the end of three years. the same machine has a value of $2,800 at the end of 8 years

Question

use the title to answer the problem.

find the average rate of change (depreciation) of the machine between its purchase and the end of 3 years.

Answer 1

Original cost of machine is $15,600.

After t=3 years, the value has decreased to $7500.

The rate of depreciation over the first 3 years can be modelled as

7500 = 15,600*(1-r)³, where r is the rate of depreciation.

Divide both sides by 15,600.

0.4808 = (1-r)³.

Take the cube root of both sides.

0.4808^1/3 = 1-r.

Solve for r.

r = 1 - 0.4808^1/3 = 1 - 0.7834 = 0.2166.

Over the first 3 years, the rate of depreciation averages to 0.2166 (21.66%)