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Exponential Growth and Decay

Exponential Growth and Decay. Exponential Growth. A = P ( 1 + r ) t A: Amount after time t P: Principle (starting amount) t: Time after starting point r: Decimal increase (% ÷ 100). Exponential Decay. A(t) = P ( 1 – r ) t A(t): Amount as a function in terms of t

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Exponential Growth and Decay

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  1. Exponential Growth and Decay

  2. Exponential Growth A = P ( 1 + r ) t A: Amount after time t P: Principle (starting amount) t: Time after starting point r: Decimal increase (% ÷ 100)

  3. Exponential Decay A(t) = P ( 1 – r ) t A(t): Amount as a function in terms of t P: Principle (starting amount) t: Time after starting point r: Decimal decrease (% ÷ 100)

  4. Growth and Decay The area of a rain forest is 20,000,000 square miles. Every year, 11% of the rain forest will be destroyed. Write an equation that will find the remaining area y of the rain forest after x years. y = 20,000,000 ( .89 )x

  5. Growth and Decay Bailey is going to put $10,000 into a bank account. Every year the value of the account will increase by 8%. Write a function V that will determine the value of the account after x years. V(x) = 10,000 ( 1.08 )x

  6. Growth and Decay The population of people in Upper Darby is 2,000,000. Every year the population will decrease by 19%. Write an equation y that will predict the population after x years. y = 2,000,000 ( .81 )x

  7. Growth and Decay The value of a home worth $165,000 will increase by 3.5% every year. Write a function V that will predict the value of a home after x years. V(x) = 165,000 ( 1.035 )x

  8. A population of 20 rabbits is released into a wildlife region. The population triples each year. • How many bunnies • Are there in 5 years? • When will the • Bunny population • reach 1000?

  9. You try: • 2) Collin’s business had a profit of $25,000 in 1998. If the profit increased by 12% each year, what would his expected profit be in the year 2010? • 3) How long did it take the profit to double?

  10. Sophia invests $1000 in a company. After 5 years your investment is worth $2125. What is the rate of her return? • She invested $1000 in another company and 5 years later she only has $625. What is her rate of return for this company?

  11. Iodine-131 is a radioactive isotope used in medicine. Its half-life or decay rate of 50% is 8 days. If a patient is given 25mg of iodine-131, how much would be left after 32 days or 4 half-lives.

  12. Compound Interest Formula • P dollars invested at an annual rate r, compounded n times per year, has a value of F dollars after t years. • Think of P as the present value, and F as the future value of the deposit.

  13. Examples • Josh’s credit card charges 12.2% interest compounded monthly. If he spents $220 this month, how much would his bill be at the end of 3 months? • Josh sees a credit card that offers 10.5% interest that is compounded quarterly. How much would he owe after 3 months with this card?

  14. Compounded Continuously

  15. A credit card company charges 22.99% compounded continuously. If you charged $500 this month how long would it take your bill to double?

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