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Exponential Growth and Decay

Exponential Growth and Decay. Modified from the presentation at: www.mathisnothard.com/pages/.../ powerpoint s/exp growthdecay . ppt. E XPONENTIAL G ROWTH M ODEL. W RITING E XPONENTIAL G ROWTH M ODELS. C is the initial amount. t is the time period. y = C (1 + r ) t.

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Exponential Growth and Decay

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  1. Exponential Growth and Decay Modified from the presentation at: www.mathisnothard.com/pages/.../powerpoints/expgrowthdecay.ppt

  2. EXPONENTIAL GROWTH MODEL WRITING EXPONENTIAL GROWTH MODELS C is the initial amount. t is the time period. y = C (1 + r)t (1 + r) is the growth factor,r is the growth rate.

  3. You Try: Your business had a profit of $25,000 in 1998. If the profit increased by 12% each year, what would your expected profit be in the year 2010? C = $25,000 T = 12 R = 0.12

  4. Writing an Exponential Growth Model A population of 20 rabbits is released into a wildlife region. The population triples each year for 5 years. What is the population after 5 years? SOLUTION After 5 years, the population is P = C(1 + r)t Exponential growth model = 20 • 35 = 4860 There will be about 4860 rabbits after 5 years.

  5. EXPONENTIAL DECAY MODEL WRITING EXPONENTIAL DECAY MODELS C is the initial amount. t is the time period. y = C (1 – r)t (1 – r) is the decay factor,r is the decay rate.

  6. Example: Depreciation • You buy a new car for $22,500. The car depreciates at the rate of 7% per year, • What was the initial amount invested? • What is the decay rate? The decay factor? • What will the car be worth after the first year? The second year? • The initial investment was $22,500. • The decay rate is 0.07. The decay factor is 0.93.

  7. You Try: 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. C = 25 mg T = 4 R = 0.5

  8. Continuous Compounding • We can compound every instant (i.e., continuously): • Here, F is the future value, P is the present value, r is the annual rate of interest, t is the total number of years, and e is a constant equal to about 2.718 clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

  9. Example: • Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. What is the future value of your $1,000 investment? clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

  10. Example: • Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. If you plan to leave the money in the account for 5 years, what is the future value of your $1,000 investment? clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

  11. Homework p.456, #4, 5, 6, 8, 9, 12

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