Download Analysis Quiz Chapters 3

Algebra II
Exponential Growth and Decay
Name________________
Date_________________
Directions: Solve each problem. Be sure to SHOW ALL WORK!!! Circle your
answer. This assignment is due Tuesday, June 5, 2016.
1. A colony of bacteria grows exponentially. The colony begins with 25
bacteria, but after 5 hours the beginning of the experiment, it has grown
to 120 bacteria.
a) What is the growth factor of the function used to express this
problem? (Be sure to keep your answer in radical form)
b) Exactly how long does it take the colony to grow to six times its
original size?
2.
Borat recently told me that the current population of Kazakstan is
approximately 4,700,000 people and has a continuous growth rate of
2.75%. He also informed me that the neighboring country of Uzbekistan
has a population of 3,850,000 people and has a continuous growth rate
of 3.27% With this information, determine how many years it will take
for these neighboring countries to have equal populations.
3. A bacteria colony is calculated to have 1200 cells at 12:00 in the
afternoon. Three hours later, the colony has a population of 1500 cells.
How many cells will there be at 9:00 at night?
Algebra II
Exponential Growth and Decay
Page 2
4. A biologist is researching a newly-discovered species of bacteria. At time
t = 0 hours, he puts one-hundred fifty bacteria into what he has
determined to be a favorable growth medium. Six hours later, he
measures 450 bacteria. Assuming exponential growth, what is the growth
constant "b" for the bacteria? (Round b to two decimal places.)
5. A rubber ball is dropped onto a hard surface from a height of 9 feet, and
it bounces up and down. At each bounce, the ball rises to 74% of its
previous height.
a) How high will the ball bounce after the 8th bounce?
b) How many bounces will it take before the ball rises no higher than
3 inches?
6. A 15-g sample of radioactive iodine decays in such a way that the mass
remaining after t days is given by m(t )  15e .087t , where m is measured in
grams. After how many days is there only 6 grams remaining?
Algebra II
Exponential Growth and Decay
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7. The exponential growth model A  25e 0.198026t describes the population of
a city in the United States, in thousands, t years after 1994. Use this
model to solve the following:
a What was the population of the city in 1994?
b By what % is the population of the city increasing each year?
c What will the population of the city be in 2005?
d When will the city’s population be 60 thousand?
8. The Philadelphia Art Museum recently purchased a bronze statue of Mr.
C for $400,000.
After having it appraised, they learned that, on
average, it will lose 10% of it’s value every year.
a) Estimate the value of the statue after 6 months.
b) Estimate the value of the statue after 3 months.
c) Estimate how many years it will take before the statue is worth
half of its purchase price.
9. The population of Mexico was 100.4 million in 2000 and is expected to
grow exponentially at a rate of 1.4% per year.
a) Estimate Mexico’s population in 2010.
b) When will Mexico’s population reach 125 million?
Algebra II
Exponential Growth and Decay
Page 4
10. Suppose that the population of a colony of bacteria increases
exponentially. At the start of an experiment, there are 6,000 bacteria,
and one hour later, the population has increased to 6,400. How long will it
take for the population to reach 10,000? Round your answer to the
nearest hour.
11.
Suppose that at the start of an experiment there are 8,000 bacteria. A
growth inhibitor and a lethal pathogen are introduced into the colony.
After two hours 1,000 bacteria are dead. If the death rates are
exponential, (a) how long will it take for the population to drop below
5,000? (b) How long will it take for two-thirds of the bacteria to die?
Round your answers to the nearest tenth.
12. Matt bought a new car at a cost of $25,000. The car
depreciates approximately 15% of its value each year.
a.) What is the decay factor for the value of this car?
b.) Write an equation to model the decay value of this car.
c.) What will the car be worth in 10 years?