Important: enter your name above, Answer the questions below. You should use the Equation Editor to write mathematical expressions and equations. You must show your work & explain your answers in order to receive full credit.
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.
1. Rational Equations
The cost, in millions of dollars, to remove x % of pollution in a lakeis modeled by
[Note: in the formula for x, you must use 70, and not 0.75, a common error]
a. What is the cost to remove 50% of the pollutant?
b. What is the cost to remove 70 % of the pollutant?
c. What is the cost to remove 90% of the pollutant?
d. What is the cost to remove 99% of the pollutant?
e. For what value is this equation undefined?
f. Do the answers you got match your expectations? Why or why not?
(Source: Sea World )
2. Ratios & Proportions
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 $3,600 for setup costs and $4.00 to administer each test.
a. Write an expression that gives the total cost to test x animals.
b. Find the average cost per animal by dividing total costs by number of animals. Write an algebraic expression that gives the average cost per animal.
c. Find the average cost per animal for 10 animals. 100 animals. 1,000 animals.
d. Explain what happens to the average cost to test the animals as the number of animals tested increases? Can the average cost ever fall below $4.00? 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 $8.00 per animal?
3. Direct or Inverse Proportionality
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.
b. A biologist counted the number of white tail deer in a 250 acre parcel of land in a nature preserve and found 20 deer.
Find the constant of variation k.
c. If the entire nature preserve is 6000 acres, then what is the total white tail deer population in the preserve? Describe how you arrived at your answer.
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