growth and decay problem

Question

1. A company purchases a new machine for $3,000.  The value of the machine depreciates (the amount it's worth decreases) at a rate of 10% each year.

 

1. How much is the machine worth after 4 years?

 

1. How much is the machine worth after 6 years?

 

1. In what year is the machine worth $1,046?

 

1. Justify your solution.

Answer 1

The depreciation of 10% means that the machine is worth 90% of its previous year's value. After 4 years the depreciation is 0.9^4=0.6561, so applying this to $3,000=$1,968.30.

After a further 2 years this comes to $1,594.32.

The depreciation to $1,046 is 1046/3000=0.34867 approx. To find out how many years this is, we need logarithms: x=log0.34867/log0.9=10 years.