1 / 11

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.

spike
Télécharger la présentation

Exponential Growth and Decay

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related