Question

Q9 QUESTION 9 THIS IS NOT GRADED ASSIGNMENT THANK YOU

Answer 1

Step-by-step 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;

`(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} (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)

`(\ln 3)/(\ln (1.1163))=t`

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

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

ANSWER:

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