To model the given problem, we use the following exponential function:
[tex]V(t)=500,000(1-0.0552)^t.[/tex]Now, we set the above equation to
[tex]V(t)=\frac{500,000}{2}=250,000=500,000(1-0.0552)^t.[/tex]Solving for t, we get:
[tex]\begin{gathered} \frac{250,000}{500,000}=0.9448^{t,} \\ tln(0.9448)=ln(\frac{1}{2}), \\ t=\frac{ln(\frac{1}{2})}{ln(0.9448)}. \end{gathered}[/tex]Finally, we get:
[tex]t\approx12\text{ years.}[/tex]