Chapter 7.4, Problem 49E

To determine

To find multiple choice. For time it takes the value of the account to triple.

Answer to Problem 49E

It takes 11.1 years of the account to triple. Option (D).

Explanation of Solution

Given information: A bank account earning continuously compounded interest doubles in the value in 7.0 years.

(A) 4.4 years

(B) 9.8 years

(C) 10.5 years

(D) 11.1 years

(E) 21.0 years

Calculation: The required solution is obtained as,

Using the law of Exponential changes:

  $y=y_0{e}^{kt}$

We can use the equation,

  $y=2y_0$ when $t=7.0$ years

Substitute and solve:

  $\begin{array}{l}2y_0=y_0{e}^{7k}\\ 2=e^{7k}\\ \ln \left(2\right)=7k\\ k=\frac{\ln \left(2\right)}{7}\end{array}$

The account the triples, therefore,

  $y=3y_0$

So,

  $\begin{array}{l}3y_0=y_0{e}^{kt}\\ \ln \left(3\right)=kt\\ t=\frac{\ln \left(3\right)}{k}\\ =\frac{7\ln \left(3\right)}{\ln \left(2\right)}\\ =11.1\end{array}$

Hence, it take 11.1 years of the account to triple. Option (D).