Question

A piece of equipment, purchased for $2000, decreases in value by 25% each year.11) Write an exponential function to represent the value of the equipmentafter x number of years.12) What will the equipment be worth in 5 years?

Answer 1

If the equipment decreases in value by 25% each year, then the value of each year is 75% of the previous year's value. Therefore, we can compute the next table

year value

0 2000

1 2000*0.75 = 1500

2 1500*0.75 = (2000*0.75)*0.75 = 2000*0.75² = 1125

3 1125*0.75 = 2000*0.75³

Then, after x years the value is given by the next exponential function:

`y=2000\cdot0.75^x`

In 5 years,

`\begin{gathered} y=2000\cdot0.75^5 \\ y=2000\cdot0.237 \\ y=474 \end{gathered}`

the equipment will be worth $474