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Exponential Growth and Decay

Understand exponential growth and decay with practical examples such as population changes, financial investments, and radioactive decay. Learn how to calculate remaining values and predict future outcomes.

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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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