Exponential Growth and Decay

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?