Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
Given:
Doubling time,
= 7.5 years
As we know,
[tex]P(t) = P_oe^{rt}[/tex]
now,
⇒ [tex]2P_o=P_o e^{r\times 7.5}[/tex]
    [tex]2 = e^{r\times 7.5}[/tex]
    [tex]r = \frac{ln2}{7.5}[/tex]
     [tex]=0.092[/tex]
     [tex]=9.2[/tex]%
then,
⇒ [tex]P(t) = P_o e^{0.092 t}[/tex]
here,
[tex]P(t) = 5P_o[/tex]
hence,
⇒ [tex]5P_o = P_o e^{0.092 t}[/tex]
[tex]e^{0.092t}=5[/tex]
    [tex]t = \frac{ln5}{0.092}[/tex]
     [tex]=17.414 \ years[/tex]    Â
