Do Now #5 You decide to start a savings. You start with 100 dollars and every month you add 50% of what was previously there. How much will you have in 6 months?

Applications of Exponential Functions

The Formulas you need to know

Exponential Growth and Decay For exponential functions,the value of b is the growth or decay factor. You can model exponential growth or decay with this function: Amount after t time periods. Initial amount Rate of growth (r > 0) or decay (r< 0) # of time periods

You invest $1000 in a savings account at the end of 6 th grade. The account pays 5% annual interest. How much money will be in the account after six years? After 6 years the account contains $ Money Example #1

Population Example #1 A population of 1000 frogs increases at an annual rate of 5%. How many frogs will there be in 6 years?

The formula was used to calculate interest compounded annually. The formula for continuously compounded interest uses the number e. Amount in account at time t Principal Interest rate (annual) Time Compounded Continuously

Suppose you won a contest at the start of 5 th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you enter high school 4 years later? After 4 years, you have $ in the account. Money Example #2

When there are different compounding period (besides annually and “compounded continually”). Example: Determine the value of a $5000 investment with a interest rate or 4.8% with different compounding periods. Money Example #3

Different Compounding Periods a) Annually [n=1] Determine the value of a $5000 investment with a interest rate or 4.8% over the span of 10 years with different compounding periods. P=5000 | R=.048 N=1 | T=10 b) Quarterly [n=4] P=5000 | R=.048 N=4 | T=10

Different Compounding Periods c) Monthly [n=12] P=5000 | R=.048 N=12 | T=10 d) Daily [n=365] P=5000 | R=.048 N=365 | T=10

Practice Problem#1 Solving for Time Diego decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account?

Practice Problem #2 Solving for Rate If there are 20 foxes in the forest this year, and 21 in one year, what percent is the percent growth of the foxes? P=20 | A= 21 | N=1 | T=1

Practice Problem #3 Solving for Rate (when t is not 1) If there are 20 foxes in the forest this year, and 30 in 5 years, what percent is the percent growth of the foxes? P=20 | A= 21 | N=1 | T=5

Classwork Due at the end of class Page 457 #s 101, Page 469 #s 1, 3, 4, 5, 7, 35

Do Now (period 5) Classwork for 4/29 Page 457 #s 101, Classwork for 5/3 – DO NOW Page 457 #’s Page 469 #s 1, 3, 4, 5, 7, 35