Question

During a 5-year period of constant inflation, the value of a $113,000 property increases according to the equation v=113,000e0.04t dollars. In how many years will the value of this building be double its current value?

Answer 1

17.33 years.

Step-by-step explanation:

The value of the property increases according to the equation:

`v=113,000e^(0.04t)`

When the building is double its current value:

`\begin{gathered} v=2*113,000. \\ \implies2*113,000=113,000e^(0.04t) \end{gathered}`

We want to solve for t:

Divide both sides by 113,000

`\begin{gathered} (2*113,000)/(113,000)=(113,000e^(0.04t))/(113,000) \\ 2=e^(0.04t) \end{gathered}`

Take the natural logarithm (ln) of both sides:

`\begin{gathered} \ln (2)=\ln (e^(0.04t)) \\ \ln (2)=0.04t \end{gathered}`

Finally, divide both sides by 0.04:

`\begin{gathered} (\ln (2))/(0.04)=(0.04t)/(0.04) \\ t=17.33 \end{gathered}`

In 17.33 years, the value of the building will double its current value.