Unit 5 Exponential Word Problems Part 2 COMPOUND

Unit 5: Exponential Word Problems – Part 2 COMPOUND INTEREST: P = Principal Amount r = annual interest rate (decimal of percent) n = # of times interest compounded in a year 1) A principal of $2000 in an account that pays 10% annual interest, and the interest is compounded quarterly. How much money is in the account after 3 years? 2) A principal of $3500 in an account that pays 7% annual interest, and the interest is compounded monthly. How much money is in the account after 3 years?

3) A principal of $4000 in an account that pays 12% annual interest, and the interest is compounded weekly. How much money is in the account after 3 years? 4) A principal of $3500 in an account that pays 7% annual interest, and the interest is compounded daily. How much money is in the account after 7 years? 5) $2400 is invested into an account that pays 3. 5% annual interest, and the interest is compounded monthly. How much money is in the account after 1. 5 years? 6) A principal of $700 in an account that pays 6% annual interest, and the interest is compounded daily. How much money is in the account after 8 years?

COMPOUNDED CONTINUOUSLY [A] Suppose you deposit $700 into an account paying 6% compounded continuously. i) How much will you have after 8 years? ii) How long will it take to have at least $2000? (round to the tenth of a year)

[B] Suppose you deposit $1000 into an account paying 5% compounded continuously. i) How much will you have after 10 years? ii) How long will it take to triple your money? (round to the tenth of a year)

UNIT 5 (10. 6): EXPONENTIAL GROWTH AND DECAY CONTINUOUS Exponential Growth and Decay Percent of change is continuously occurring during the period of time (yearly, monthly, …) Examples: “Continuous Interest”, “Radioactive Half-Life” y = final amount a = original amount k = growth rate constant t = time

Example 1 Continuous Exponential Growth a) A population of rabbits is growing continuously at 20% each month. If the colony began with 2 rabbits, how many months until they reach 10, 000 rabbits? b) Jill invested $1000 into a CD account that claims to compound continuously at 10%. How long will it take triple her investment?

Example 1 Continuous Exponential Growth c) As of 2000, the populations of China and India can be modeled by C(t) = 1. 26 e 0. 009 t and I(t) = 1. 01 e 0. 015 t. According to the models, when will India’s population be more than China’s?

Example 1 Continuous Exponential Growth d) The population of Raleigh was 212, 000 in 1990 and was 259, 000 in 1998. Write a continuous exponential growth equation, where t is the numbers of years after 1990 for Raleigh’s population. e) Based on part e), What is the predicted population of Raleigh this year?

Example 2 Continuous Exponential Decay #1: Why is the formula for the half life of Carbon-14 The half-life of Carbon-14 is 5760 years which means that every 5760 years half of the mass decays away. 1 a) A paleontologist finds the bones of a Wooly Mammoth. She estimates the bones only contain 4% of the Carbon-14 that it would have had alive. Estimate the age of the Mammoth.

1 b) A paleontologist finds that the Carbon-14 of a bone is 1/12 of that found in living bone tissue. What is the age of the bone? #2: The half life of Sodium-22 is given below. A geologist is studying a meteorite and estimates that it contains only 12% of as much Sodium-22 as it would have when it reached the earths atmosphere. How long ago did the meteorite reach earth.

#3: Radioactive iodine decays according to the equation where t is in days. Find the half-life of the substance. #4: The half life of Radium-226 is 1800 years. Find the half-life equation for Radium-226. ,