Question

A typical combine harvester sells for $500,000. If the value of the combine depreciates 5.52% each year, how many years will it take to lose half of it's value? Round your answer to the nearest whole number of years.

Answer 1

To model the given problem, we use the following exponential function:

`V(t)=500,000(1-0.0552)^t.`

Now, we set the above equation to

`V(t)=(500,000)/(2)=250,000=500,000(1-0.0552)^t.`

Solving for t, we get:

`\begin{gathered} (250,000)/(500,000)=0.9448^(t,) \\ tln(0.9448)=ln((1)/(2)), \\ t=(ln((1)/(2)))/(ln(0.9448)). \end{gathered}`

Finally, we get:

`t\approx12\text{ years.}`

Answer:

`12\text{ years.}`