Associate Level Material
Appendix D
The Environment
Environmental and wildlife preservation ensures future generations will have available resources and can
enjoy the beauty of Earth. On the other hand, some of the damage humans have already done to the
environment is expensive and time consuming to eradicate.
Application Practice
Answer the following questions. Use Equation Editor to write mathematical expressions and equations.
First, save this file to your hard drive by selecting Save As from the File menu. Click the white space
below each question to maintain proper formatting.
1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C 
6,000
200  2 x
a. What is the cost to remove 75% of the pollutant?
Answer:
C
6000
 $120
200  2  75
b. What is the cost to remove 90% of the pollutant?
Answer:
C
6000
 $300
200  2  90
c. What is the cost to remove 99% of the pollutant?
Answer:
C
6000
 $3000
200  2  99
d. For what value is this equation undefined?
Answer:
For x = 100%.
It is because when x equals to 100%, the denominator of the rational function is 0 which
makes the equation undefined.
e. Do the answers to sections a. through d. match your expectations? Explain why or why
not.
Answer:
Yes, because the cost will be more to remove a larger percent of pollutants. They are directly
proportional related.
MAT/117
Busch Enteratinment Corporation. (N.D.). Flamingos. Retrieved from
http://www.seaworld.org/animal-info/info-books/flamingo/physical-characteristics.htm
2. Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that
the costs for such a station are $2,500 for setup costs and $3.00 to administer each test.
a. Write an expression that gives the total cost to test x animals.
Answer:
Let x be the number of animals and C be the cost
C(x) = 2500 + 3x
b. You can find the average cost per animal by dividing total costs by number of animals.
Write the expression that gives the average cost per animal.
Answer:
Average cost per animal =
c.
C ( x) 2500  3x

x
x
Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals.
Answer:
Average cost per animal for 10 animals =
2500  3  10
 $253
10
Average cost per animal for 100 animals =
Average cost per animal for 1000 animals =
2500  3  100
 $28
100
2500  3  1000
 $5.5
1000
d. As the number of animals tested increases, what happens to the average cost to test the
animals? Would the average cost ever fall below $3.00? If so, identify a value that
supports your answer. If not, explain how you know.
Answer:
As x (the number of animals) get larger and larger, 2500 in the rational function becomes
irrelevant. The average cost becomes $3x/x which is equals to $3. Therefore, the value
will approach to $3 but never fall below $3.
e. How many animals should be tested for the average cost to be $5.00 per animal?
Answer:
2500  3 x
5
x
2500  3 x  5 x
2 x  2500
x  1250
Therefore, 1250 animals should be tested.
MAT/117
3. To estimate animal populations, biologists count the total number of animals in a small section of
a habitat. The total population of animals is directly proportional to the size of the habitat (in
acres) polled.
a. Write an equation using only one variable that could be used to solve for the constant of
variation k.
Answer:
Let P be the population and x be the size of the habitat
P= kx
b. A biologist counted 12 white tail deer in a 100-acre parcel of land in a nature preserve.
Find the constant of variation k.
Answer:
12=k * 100
K=0.12
c.
If the entire nature preserve is 2,500 acres, then what is the total white tail deer
population in the preserve? Describe how you arrived at your answer.
Answer:
P=0.12 * 2500
P=300
I arrived my answer based on the equation and the value of k calculated from part(a) and
part (b) above.
MAT/117