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Exponential Growth and Decay

Exponential Growth and Decay. Section 3.5. Objectives. Solve word problems requiring exponential models. Find the time required for an investment of $5000 to grow to $6800 at an interest rate of 7.5% compounded quarterly.

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Exponential Growth and Decay

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  1. Exponential Growth and Decay Section 3.5

  2. Objectives • Solve word problems requiring exponential models.

  3. Find the time required for an investment of $5000 to grow to $6800 at an interest rate of 7.5% compounded quarterly.

  4. The population of a certain city was 292000 in 1998, and the observed relative growth rate is 2% per year. • Find a function that models the population after t years. • Find the projected population in the year 2004. • In what year will the population reach 365004?

  5. The count in a bacteria culture was 600 after 15 minutes and 16054 after 35 minutes.  Assume that growth can be modeled exponentially by a function of the form where t is in minutes. • Find the relative growth rate. • What was the initial size of the culture? • Find the doubling period in minutes. • Find the population after 110 minutes. • When will the population reach 15000?

  6. The half-life of strontium-90 is 28 years.  Suppose we have a 80 mg sample. • Find a function that models the mass m(t) remaining after t years. • How much of the sample will remain after 100 years? • How long will it take the sample to decay to a mass of 20 mg?

  7. A wooden artifact from an ancient tomb contains 35% of the carbon-14 that is present in living trees.  How long ago was the artifact made?  (The half-life of carbon-14 is 5730 years.)

  8. An infectious strain of bacteria increases in number at a relative growth rate of 190% per hour.  When a certain critical number of bacteria are present in the bloodstream, a person becomes ill.  If a single bacterium infects a person, the critical level is reached in 24 hours.  How long will it take for the critical level to be reached if the same person is infected with 10 bacteria?

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