Question

T equals blank years. Do not round until the final answer then round to one decimal place as needed

Answer 1

Given

• Amount invested (,P,): $9500

• Annual interest rate (,r,): 10% = 0.1

$10\%=\frac{10}{100}=0.1$

• Accumulated amount (,A,): $19000 because it is double the amount invested.

• Time (,t,): ? years.

Explanation

We replace the know values in the below formula, and we solve for t.

$\begin{gathered} A=Pe^{rt} \\ 19000=9500e^{0.1t} \\ \text{ Divide by 9500 from both sides} \\ \frac{19000}{9500}=\frac{9500e^{0.1t}}{9500} \\ 2=e^{0.1t} \\ \text{ Apply natural logarithm from both sides} \\ \ln(2)=\ln(e^{0.1t}) \\ \text{ Applt the property }\ln(e^x)=x,\text{ for x > 0} \\ \ln(2)=0.1t \\ \text{ Divide by 0.1 from both sides} \\ \frac{\operatorname{\ln}(2)}{0.1}=\frac{0.1t}{0.1} \\ 6.9\approx t \\ \text{ The symbol }\approx\text{ is read 'approximately'} \end{gathered}$Answer

The time it takes to obtain the accumulated amount is approximately 6.9 years.