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Advanced Precalculus Notes 4.8 Exponential Growth and Decay

Advanced Precalculus Notes 4.8 Exponential Growth and Decay. k > 0 growth k < 0 decay. A colony of bacteria grows according to the law of uninhibited growth according to the function , where N is measured in grams and t is measured in days.

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Advanced Precalculus Notes 4.8 Exponential Growth and Decay

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  1. Advanced Precalculus Notes 4.8 Exponential Growth and Decay k > 0 growth k < 0 decay

  2. A colony of bacteria grows according to the law of uninhibited growth according to the function , where N is measured in grams and t is measured in days. a) What is the initial amount of bacteria? b) What is the growth rate of the bacteria? c) Graph the function on the calculator. d) What is the population after 5 days? e) How long will it take for the population t reach 140 grams? f) What is the doubling time for the population?

  3. A colony of bacteria increases according to the law of uninhibited growth. k > 0 a) If the number of bacteria doubles in 3 hours, write the function that gives the number of cells in the culture. b) How long will it take for the size of the colony to triple?

  4. Traces of burned wood along with ancient stone tools in an archeological dig in Chile were found to contain ≈ 1.67% of the original amount of carbon 14. k < 0 a) If the half-life of carbon 14 is 5600 years, approximately when was the tree cut and burned? b) Using a graphing calculator, graph the relation between the percentage of carbon 14 remaining and time. c) Determine the time that elapses until half of the carbon 14 remains. (half-life of carbon 14)

  5. Logistic Model b > 0 growth b < 0 decay Fruit flies are placed in a half-pint milk bottle with food. The population after t days is: a) State the carrying capacity and the growth rate. b) Determine the initial population. c) Graph P(t) d) What is the population after 5 days? e) How long does it take for the population to reach 180? f) How long does it take for the population to reach one-half of the carrying capacity?

  6. Assignment: page 334: 1, 4, 9, 21, 27

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