Exponential Growth and Decay

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Exponential and Logistic Modeling

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Presentation transcript:

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.

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?

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?

The half-life of strontium-90 is 28 years 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?

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.)

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?