Answer:
17.33 years.
Explanation:
The value of the property increases according to the equation:
[tex]v=113,000e^{0.04t}[/tex]
When the building is double its current value:
[tex]\begin{gathered} v=2\times113,000. \\ \implies2\times113,000=113,000e^{0.04t} \end{gathered}[/tex]
We want to solve for t:
Divide both sides by 113,000
[tex]\begin{gathered} \frac{2\times113,000}{113,000}=\frac{113,000e^{0.04t}}{113,000} \\ 2=e^{0.04t} \end{gathered}[/tex]
Take the natural logarithm (ln) of both sides:
[tex]\begin{gathered} \ln (2)=\ln (e^{0.04t}) \\ \ln (2)=0.04t \end{gathered}[/tex]
Finally, divide both sides by 0.04:
[tex]\begin{gathered} \frac{\ln (2)}{0.04}=\frac{0.04t}{0.04} \\ t=17.33 \end{gathered}[/tex]
In 17.33 years, the value of the building will double its current value.
