8.2 years
Explanation:
Initial amount = $800
Doubling the amount = 2(800) = $1600
Future amount = double the amount = $1600
rate = 8.5% = 0.05
time = t = ?
n = compounded continously
The function is given as:
[tex]A=800e^{0.085t}[/tex]
We need to find the time given the amount is $1600:
[tex]\begin{gathered} 1600=800e^{0.085t} \\ \text{divide both sides by 800:} \\ \frac{1600}{800}\text{ = }\frac{800e^{0.085t}}{800} \\ 2\text{ = }e^{0.085t} \\ \\ \text{Taking natural log of both sides:} \\ \log _e\text{ 2= }\log _e\text{ }(e^{0.085t}) \\ \log _e\text{ 2 = 0.085t} \end{gathered}[/tex][tex]\begin{gathered} \log _e\text{ = ln} \\ \log _e\text{ 2 = ln 2} \\ \ln 2\text{ = 0.085t} \\ divide\text{ both sides by 0.085:} \\ \frac{\ln \text{ 2}}{0.085\text{ }}\text{ = }\frac{\text{0.085t}}{0.085} \\ 8.1547\text{ = t} \\ \\ To\text{ the nearest tenth of a year, t = 8.2 years} \end{gathered}[/tex]
