Practice #1 - Exponential Decay
Phosphorus-32 is used to study a plant's use of fertilizer. It has a half-life of 14.3 days. Write an exponential decay function for 100-mg sample. How much phosphorus-32 remains after 42 days (round answer to the nearest tenth).
(a) What is the initial amount of fertilizer? mg
Answer: 100 mg
(b) What is the decay factor?
Answer: 0.5
(c) Write an equation to model the fertilizer decay over a given period of time.
y = 100( ) ^(x/ )
Answer: 100(0.5)^(x/14.3)
(d) How much fertilizer is left after 42 days? mg
Answer: 13.1 mg
Practice #2 - Exponential Decay
Country B has been experiencing a decline in population. The initial population of Country B was 28,900. The population has been decreasing at a rate of 2.6% per year.
What will the population be after 20 years? First, identify the variables.
a =
b =
x =
Answer:
a = 28,900
b = 0.974
x = 20
Now, solve. Round your answer to the nearest person.
y = abx =
Answer = 17,064
Practice #3 - Exponential Decay
The population of a North Alabama city was 4,403 in 2010. This city has been experiencing a population decline of 0.06% per year since 2000.
What will be the projected population for this city in 2015? First, identify the variables
a =
b =
x =
Answer:
a = 4,403
b = 0.9994
x = 5
Now, solve. Round your answer to the nearest person.
y = abx =
Answer: y = 4,390
Practice #4 - Exponential Decay
The half-life of a certain radioactive substance is 65 days. There are 3.5 g present initially.
How much of this radioactive material will be left after 75 days? First, identify the variables.
a =
b =
x =
Answer:
a = 3.5
b = 0.5
x = 75
Now, solve. Round your answer to the nearest tenth of a gram.
y = abx =
Answer: y = 1.6 g
Practice #5 - Exponential Growth
A certain strain of bacteria doubles every 4 minutes. Assuming that you start with only one bacterium, how many bacteria could be present at the end of 72 minutes?
(a) What is the initial amount of bacteria?
Answer: 1
(b) What is the growth factor?
Answer: 2
(c) Write an equation to model the bacteria growth over a given period of time.
y = 1( ) ^(x/ )
Answer: 1(2)^(x/4)
(d) To the nearest bacterium, how many bacteria are present after 72 minutes?
Answer: 262,144
Practice #6 - Exponential Growth
The population of a Florida city was 736,000 in 2000. The population of this city is increasing at a rate of 1.49% per year.
What will the population of this city be in 2010? First, identify the variables.
a =
b =
x =
Answer:
a = 736,000
b = 1.0149
x = 10
Now, solve. Round your answer to the nearest person.
y = abx =
Answer: y = 853,317
Practice #7 - Exponential Growth
At the start of an experiment, there are 100 bacteria. If the bacteria follow an exponential growth pattern with a growth rate of 4%, what will the population be after 5 hours (round to the nearest bacteria)?
First, identify the variables.
a =
b =
x =
Answer:
a = 100
b = 1.04
x = 5
Now, solve. Round your answer to the nearest bacterium.
y = abx =
Answer: y = 122
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