Question

For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. Suppose an investment account is opened with an initial deposit of $\$ 12,000$ earning 7.2$\%$ interest compounded continuously. How much will the account be worth after 30 years?

Name: Problem 42, Chapter 4: Precalculus
Uploaded: 2019-08-08T18:56:54-08:00
Duration: 2 min 31 s
Channel: Margaret Hubacher
Description: For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. Suppose an investment account is opened with an initial deposit of 12,000 earning 7.2% interest compounded continuously. How much will the account be worth after 30 years?

   For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.
Suppose an investment account is opened with an initial deposit of $\$ 12,000$ earning 7.2$\%$ interest compounded continuously. How much will the account be worth after 30 years?

Precalculus

Jay Abramson 1st Edition

Chapter 4, Problem 42

Instant Answer

Solved by Expert Margaret Hubacher

08/08/2019

Step 1

- $P$ is the principal amount (the initial amount of money). - $r$ is the annual interest rate (in decimal). - $t$ is the time the money is invested for in years. Show more…

Show all steps

Thanks for your feedback!

For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. Suppose an investment account is opened with an initial deposit of $\$ 12,000$ earning 7.2$\%$ interest compounded continuously. How much will the account be worth after 30 years?

Play audio

Feedback

Margaret Hubacher and 94 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Continuous Compounding

Continuous compounding refers to the process in which interest is calculated and added to the principal an infinite number of times per period. It is modeled with the formula A = P e^(rt), where P is the initial principal, r is the constant interest rate, and t is time. This method of compounding results in exponential growth when the rate is positive.

Exponential Growth and Decay

Exponential growth or decay describes processes where the rate of change of a quantity is proportional to its current value, leading to exponential functions. In the context of continuous compounding, a positive rate (r > 0) results in exponential growth, as the value increases continuously over time, while a negative rate (r < 0) results in exponential decay.

Please give Ace some feedback