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Axia College Material

Appendix D

The EnvironmentEnvironmental and wildlife preservation ensures future generations will have available resources and canenjoy the beauty of Earth. On the other hand, some of the damage humans have already done to theenvironment 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 Filemenu. Click the white spacebelow each question to maintain proper formatting.

1. The cost, in millions of dollars, to removex% of pollution in a lake modeled byx

C2200

000,6

=

a. What is the cost to remove 75% of the pollutant?75*2200

6000

=C C= 120 million

b. What is the cost to remove 90% of the pollutant?90*2200

6000

=C C= 300 million

c. What is the cost to remove 99% of the pollutant?99*2200

6000

=C C= 3000 million

d. For what value is this equation undefined?100*2200

6000

=C C=undefined

e. Do the answers to sections a. through d. match your expectations? Explain why or whynot. == Yes! These values do match what I would expect. As we remove more pollution,the cost will goes up. We are not able to remove all of the pollution, so there is no amountof money to do it

Busch Enteratinment Corporation. (N.D.). Flamingos. Retrieved fromhttp://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 thatthe 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 testxanimals. cost = 3x + 2500

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. avg cost = (3x+2500)/x

c. Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals.

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http://www.seaworld.org/animal-info/info-books/flamingo/physical-characteristics.htmhttp://www.seaworld.org/animal-info/info-books/flamingo/physical-characteristics.htmhttp://www.seaworld.org/animal-info/info-books/flamingo/physical-characteristics.htm

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10 animals.Plug in x = 10avg cost = (3*10+2500)/10= 253 dollars

100 animals.Plug in x = 100avg cost = (3*100+2500)/100= 28 dollars

1,000 animals.Plug in x = 1000avg cost = (3*1000+2500)/1000= 5.5 dollars

d. As the number of animals tested increases, what happens to the average cost to test theanimals? Would the average cost ever fall below $3.00? If so, identify a value thatsupports your answer. If not, explain how you know.

No! The average cost to test the animals will goes down towards $3 as we test more and more animals.But, the average cost cannot go below $3 since we always have to add on the fixed cost of $2500 and the$3 per animal.

e. How many animals should be tested for the average cost to be $5.00 per animal?

x

x 250035

+= X= 1250

3. To estimate animal populations, biologists count the total number of animals in a small section ofa habitat. The total population of animals is directly proportional to the size of the habitat (inacres) polled.

a. Write an equation using only one variable that could be used to solve for the constant ofvariation k.

kSA =

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.

10012 = k k=0.12

c. If the entire nature preserve is 2,500 acres, then what is the total white tail deerpopulation in the preserve? Describe how you arrived at your answer.

Use the original equation with k = 0.12 2500*12.0*12.0 == sa a=300 deer

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