Question

Q9 QUESTION 9 THIS IS NOT GRADED ASSIGNMENT THANK YOU

Answer 1

EXPLANATION:

We are given an investment that tripples in value at tha rate of 11% annually compounded contnuously.

Note the following details from the question;

$\begin{gathered} \text{ Principal}=P \\ \text{Amount}=3P\text{ (tripple the principal)} \\ r=11\%\text{ (OR 0.11)} \\ t=\text{?} \end{gathered}$

We shall use the formula for continuous compounding which is;

$A=Pe^{rt}$$3P=Pe^{0.11^{}t}$$3P=P(e^{0.11})^t$

Divide both sides by P;

$\frac{3P}{P}=(e^{0.11})^t$

Note that e is a mathematical constant whose approximate value is;

$e=2.7183\ldots$

We now have the equation refined as;

$\begin{gathered} \frac{3P}{P}=(e^{0.11^{}})^t \\ 3=(1.1163)^t \end{gathered}$

We can now apply the rule of exponents;

$\ln 3=\ln (1.1163)^t$

We now divide both sides by ln(1.1163)

$\frac{\ln 3}{\ln (1.1163)}=t$

Next we can now solve for the value of t with the use of a calculator;

$t=\frac{\ln 3}{\ln (1.1163)}$$\begin{gathered} t=\frac{1.0986}{0.11002} \\ t=9.9855 \end{gathered}$

ANSWER:

$\begin{gathered} \text{Exact length of time:} \\ t=\frac{\ln 3}{\ln (1.1163)} \\ \text{Length of time (to 2 decimal places):} \\ t=9.96 \end{gathered}$