1. Doubling & Halving Exponential Functions with Base 2 Exponential Growth y = a ∙ 2 x y is the amount after x doubling periods a is the original amount when x = 0. The value of a cannot equal 0 x is the number of doubling periods

2. Doubling & Halving Example Use the equation y = 58 ∙ 2 x Find the value of y for each value of x 1. x = 0 1. x = 0 2. x = 5 2. x = 5 3. x = 10 3. x = 10 4. x = 20 4. x = 20

3. Doubling & Halving You have $500 invested in an account which will double your money every 6 years. You have $500 invested in an account which will double your money every 6 years. a. Write the function which models the amount of money in the account. b. How much will be in the account 10 years from now? c. How long will it take to have $10,000?

4. Doubling & Halving Example Suppose Alfonso invests $2500 in a mutual fund at age 25. If the value of his investment doubles every seven years, what will be the value if the fund when Alfonso is 60 years old?

5. Doubling & Halving Example Alfonso invests $2500 in a mutual fund at age 25. The value will $80,000 when he is 60 years old

6. Doubling & Halving Biology Biology A type of bacteria reproduces by dividing into two bacteria every 20 minutes. If you start with one bacterium, how many bacteria will there be after one hour? After 2 hours? A type of bacteria reproduces by dividing into two bacteria every 20 minutes. If you start with one bacterium, how many bacteria will there be after one hour? After 2 hours?

7. Doubling & Halving Exponential Functions with Base 1/2 Usually known as half-life THIS IS EXPONENTIAL DECAY y = a ∙ (1/2) x y is the amount after x halving periods a is the original amount when x = 0. The value of a cannot equal 0 x is the number of halving periods

8. Doubling & Halving One form of radioactive iodine has a half-life of about 8 days. a. Write an equation that models the exponential decay of 500 g of this form of radioactive iodine. b. How long will it be before only 50 g of the radioactive iodine is left?

9. Doubling & Halving Suppose a radioactive substance has a half-life of about 30 days. a. Write an equation that models the exponential decay of 10 g of this form of radioactive iodine. b. How long will it be before only 1 g of the radioactive iodine is left?

10. Doubling & Halving Most medicines are gradually broken down by the body; the amount in the bloodstream decays exponentially. For example, a certain medication has a half-life in the bloodstream of 2 hr. The prescribed dosage for this medicine is 3 mg. a. Write a function that models this situation b. How much of this medicine is left in the bloodstream after 5 hr?

11. Doubling & Halving SPORTS – There are 64 teams in the first round of an NCAA basketball championship. In each round, every team in the round plays a game against one other team in the round. Only the winning team advance to the next round. a. Explain why the number of teams in each round can be modeled by an equation that represents exponential decay. b. Write an exponential equation that you can use to find the number in any round. c. What does the exponent in your equation represent?

12. Doubling & Halving A certain medication has a half-life in the bloodstream of 2 hr. The prescribed dosage for this medicine is 3 mg. A certain medication has a half-life in the bloodstream of 2 hr. The prescribed dosage for this medicine is 3 mg. a. How much of the medicine is left in the bloodstream after 45 minutes? b. How many half-lives does it take for the amount of the medicine in the bloodstream to be less than 0.01 mg? c. What would be the answer if the prescribed dosage was 5mg instead?