8 – 3 The Number e Day 2
This lesson covers the laws of fractional exponents and their applications in exponential functions, particularly in real-life contexts such as compound interest and radioactive decay. Students will learn how to use the continuous compound interest formula to calculate account balances and model exponential growth and decay. Real-world examples, including a bank deposit compounded continuously and the decay of radon-222, will be analyzed to reinforce understanding. Homework assignments from page 483 will provide additional practice on these concepts.
8 – 3 The Number e Day 2
E N D
Presentation Transcript
8 – 3 The Number eDay 2 Objective (Ca. Standard 12): Students know the laws of fractional exponents, understand exponential function, and use these functions in problems in problems involving exponential growth and decay.
Using e in Real Life Compound Interest formula Where A is the amount in the account earning interest compounded n time per year for t years, P is the principal, and r is the annual interest rate expressed as a decimal. As n approaches positive infinite, the compound interest formula approximates the following continuously compound interest
Example 4: Finding the Balance of an Account You deposit $1500 in an account that pays 7.5% annual interest rate compounded continuously. What is the balance of the account after 1 year? Solution: Note P = 1500, r = 0.075, and t = 1
Example 5: Using an Exponential Model The radioactive decay radon-222 can be modeled by where A is the amount remaining, C is the original amount, and t is the time in days. If there are 15 mg of radon 222 sealed in a glass tube, how much will remain in the tube after 8 days?
If 10 mg remains after 5 days, how much was originally there?
Homework page 483 73-79, 81-83, 84-94(even)
