QuestionSuppose that $\$ 14.225$ is invested at an interest rate of $5.8 \%$ per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time $t$ , in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is $\mathrm{P}(\mathrm{t})=14225 e^{0.058 t}$ (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.) b) The balance after 1 year is $\$$ $\square$ (Simplify your answers. Round to two decimal places as needed.)

Studdy Solution
The doubling time $T$ for continuous compounding is given by the formula:
$T = \frac{\ln(2)}{r}$
Substitute the given interest rate:
$T = \frac{\ln(2)}{0.058} \approx \frac{0.693}{0.058} \approx 11.95$
The doubling time is approximately 11.95 years.
The exponential function is $A(t) = 14225 \cdot e^{0.058t}$ .
Balances: - After 1 year: \$15,077.68 - After 2 years: \$15,954.45 - After 5 years: \$19,000.60 - After 10 years: \$25,413.85
Doubling time: 11.95 years

View Full Solution - Free

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms