ANSWER :
The answer is 46.21 years
EXPLANATION :
From the problem, we have the growth function :
[tex]A=A_oe^{0.015t}[/tex]
Solve for t when Ao = 7,300 and A = 14,600
[tex]\begin{gathered} 14600=7300e^{0.015t} \\ \frac{14600}{7300}=e^{0.015t} \\ 2=e^{0.015t} \end{gathered}[/tex]
Take ln of both sides :
[tex]\begin{gathered} \ln(2)=\ln(e^{0.015t}) \\ \text{ Note that ln \lparen e\textasciicircum x\rparen is the same as x} \\ \text{ That will be :} \\ \ln(2)=0.015t \\ t=\frac{\ln(2)}{0.015} \\ t=46.21 \end{gathered}[/tex]
