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Question 506288: 1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by
or
a. What is the cost to remove 65% of the pollutant?
Substitute x = 65 % into the first equation
Or x = 0.65 into the second equation
It will cost million to remove 65% of the pollutant.
b. What is the cost to remove 85 % of the pollutant?
It will cost million to remove 85% of the pollutant.
c. What is the cost to remove 95 % of the pollutant?
It will cost million to remove 95% of the pollutant.
d. What is the cost to remove 99.5% of the pollutant?
It will cost dollars to remove 99.5% of the pollutant.
e. For what value is this equation undefined?
Set denominator = 0 and solve:
Equation is undefined for x =
f. Do the answers to sections a–d match your expectations? Why or why not?
(Source: Sea World 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 $8,500 for setup costs and $ 15.00 per animal to administer each test.
a. Write an expression that gives the total cost to test x animals.
Letting x = number of animals tested and C = total cost
C = Setup costs + (cost per test) times (tests)
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.
c. Find the average cost per animal for 20 animals. 50 animals. 300 animals.
Number of animals (x) Cost Simplified answer
20 test
$/ test
50 test
$/ test
300 test
$/ test
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 $15.00? If so, identify a value that supports your answer. If not, explain how you know.
e. How many animals should be tested for the average cost to be $20.00 per animal?
animals must be tested for the average cost to drop to $20.00 per animal.
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.
Letting A = number of animals, and L = amount of land (acres),
k = animals per acre
b. A biologist counted the number of mule deer in a 320 acre parcel of land in a nature preserve and found 9 deer. Find the constant of variation k.
c. If the entire nature preserve is 30,000 acres, then what is the total mule deer population in the preserve? Describe how you arrived at your answer.
Use the answer from part b,
We would expect there to be mule deer in the entire preserve.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! One question per post. Also, you used way too many spaces (i.e. question takes up too much space) and did not provide equations for some of the problems.
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