Question

The doubling time for an investment is 7.5 yeas. Find an exponential model for the growth of your money. Then find how long will take your investment to grow by factor of 5(Assume that you make an investment P)

Answer 1

Answer:

The correct answer is "17.414 years".

Step-by-step explanation:

Given:

Doubling time,

= 7.5 years

As we know,

$P(t) = P_oe^{rt}$

now,

⇒ $2P_o=P_o e^{r\times 7.5}$

       $2 = e^{r\times 7.5}$

       $r = \frac{ln2}{7.5}$

          $=0.092$

          $=9.2$%

then,

⇒ $P(t) = P_o e^{0.092 t}$

here,

$P(t) = 5P_o$

hence,

⇒ $5P_o = P_o e^{0.092 t}$

$e^{0.092t}=5$

        $t = \frac{ln5}{0.092}$

          $=17.414 \ years$