Question

A computer loses half of its value every two year. If the computer costs $75 after 6 years, how much

did the computer cost initially?

Answer 1

$600

Explanation:

This can be modeled as an exponential equation.

General form of an exponential function:
`y=ab^x`

where:

• a is the initial value
• b is the growth factor
• x is the independent variable
• y is the dependent variable

Therefore:

• a = initial cost of computer
• b = 0.5 (since the computer loses half its value)
• x = t/2 where t is the number of years ⇒ 3
• y = $75

`\implies 75=a(0.5)^3`

`\implies 75=0.125a`

`\implies a=(75)/(0.125)`

`\implies a=600`

Therefore, the computer initially cost $600.