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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.

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?