doubling & halving exponential functions with base 2 exponential growth y = a ∙ 2 x y is the...

Doubling & HalvingDoubling & Halving

Exponential Functions with Base 2Exponential Functions with Base 2

Exponential GrowthExponential Growth

y = a ∙ 2y = a ∙ 2xx

y is the amount after x doubling periodsa is the original amount when x = 0. The

value of a cannot equal 0x is the number of doubling periods


ExampleExample

Use the equation Use the equation

y = 58 ∙ 2y = 58 ∙ 2xx

Find the value of y for each value of xFind the value of y for each value of x

1. x = 01. x = 0

2. x = 52. x = 5

3. x = 103. x = 10

4. x = 20 4. x = 20


You have $500 invested in an account You have $500 invested in an account which will double your money every 6 which will double your money every 6 years.years.

a.a. Write the function which models the Write the function which models the amount of money in the account.amount of money in the account.

b.b. How much will be in the account 10 How much will be in the account 10 years from now?years from now?

c.c. How long will it take to have $10,000?How long will it take to have $10,000?


ExampleExample

Suppose Alfonso invests Suppose Alfonso invests $2500 in a mutual fund at $2500 in a mutual fund at age 25. If the value of his age 25. If the value of his investment doubles every investment doubles every seven years, what will be seven years, what will be the value if the fund when the value if the fund when

Alfonso is 60 years old?Alfonso is 60 years old?


ExampleExample

Alfonso invests $2500 in a Alfonso invests $2500 in a mutual fund at age 25. The mutual fund at age 25. The

value willvalue will

$80,000$80,000

when he is 60 years oldwhen he is 60 years old


Biology Biology

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


Exponential Functions with Base 1/2Exponential Functions with Base 1/2

Usually known as half-lifeUsually known as half-life

THIS IS EXPONENTIAL DECAYTHIS IS EXPONENTIAL DECAY

y = a ∙ (1/2)y = a ∙ (1/2)xx

y is the amount after x halving periodsa is the original amount when x = 0. The

value of a cannot equal 0x is the number of halving periods


One form of radioactive iodine One form of radioactive iodine has a half-life of about 8 days.has a half-life of about 8 days.

a.a. Write an equation that models Write an equation that models the exponential decay of 500 the exponential decay of 500 g of this form of radioactive g of this form of radioactive iodine.iodine.

b.b. How long will it be before only How long will it be before only 50 g of the radioactive iodine 50 g of the radioactive iodine is left?is left?


Suppose a radioactive substance Suppose a radioactive substance has a half-life of about 30 has a half-life of about 30 days.days.

a.a. Write an equation that models Write an equation that models the exponential decay of 10 g the exponential decay of 10 g of this form of radioactive of this form of radioactive iodine.iodine.

b.b. How long will it be before only How long will it be before only 1 g of the radioactive iodine is 1 g of the radioactive iodine is left?left?


Most medicines are gradually broken Most medicines are gradually broken down by the body; the amount in the down by the body; the amount in the bloodstream decays exponentially. bloodstream decays exponentially. For example, a certain medication has For example, a certain medication has a half-life in the bloodstream of 2 hr. a half-life in the bloodstream of 2 hr. The prescribed dosage for this The prescribed dosage for this medicine is 3 mg.medicine is 3 mg.

a.a. Write a function that models this Write a function that models this situationsituation

b.b. How much of this medicine is left in How much of this medicine is left in the bloodstream after 5 hr?the bloodstream after 5 hr?

Doubling & HalvingDoubling & HalvingSPORTS – There are 64 teams in the first round SPORTS – There are 64 teams in the first round

of an NCAA basketball championship. In of an NCAA basketball championship. In each round, every team in the round plays each round, every team in the round plays a game against one other team in the a game against one other team in the round. Only the winning team advance to round. Only the winning team advance to the next round.the next round.

a.a. Explain why the number of teams in each Explain why the number of teams in each round can be modeled by an equation that round can be modeled by an equation that represents exponential decay.represents exponential decay.

b.b. Write an exponential equation that you can Write an exponential equation that you can use to find the number in any round.use to find the number in any round.

c.c. What does the exponent in your equation What does the exponent in your equation represent?represent?


A certain medication has a half-life in A certain medication has a half-life in the bloodstream of 2 hr. The the bloodstream of 2 hr. The prescribed dosage for this medicine is prescribed dosage for this medicine is 3 mg.3 mg.

a.a. How much of the medicine is left in How much of the medicine is left in the bloodstream after 45 minutes?the bloodstream after 45 minutes?

b.b. How many half-lives does it take for How many half-lives does it take for the amount of the medicine in the the amount of the medicine in the bloodstream to be less than 0.01 mg?bloodstream to be less than 0.01 mg?

c.c. What would be the answer if the What would be the answer if the prescribed dosage was 5mg instead?prescribed dosage was 5mg instead?

doubling & halving exponential functions with base 2 exponential growth y = a ∙ 2 x y is the...

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