Expert: Richard J. Raridon - 2/9/2010

Question
Hi, 1st year in college, doing algebra II (30 years old). I'm sort of confused when it comes to math. . I have a few quaetions regarding this topic (I just want to make sure I am on the right page). Here are a few questions that I am troubled with:1.   The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C=6000/200-2X (for each of the % below, would I substitute for x? (for example, 200-2(.75)).
                                 
a.   What is the cost to remove 75% of the pollutant?

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

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

d.   For what value is this equation undefined?

Also: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.

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 10 animals, 100 animals, and 1,000 animals.

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.

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

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.

c.   If the entire nature preserve is 2,500 acres, then what is the total white tail deer population in the preserve?

Answer
1. You need to write it C = 6000/(200-2x)
a. x = 75, C = 120
b. x = 90, C = 300
c. x = 99, C = 3000
d. x = 100
2. a. C = 2500+3x
b. AC = (2500+3x)/x
c. x=10, AC=253, x=100, AC=28, x=1000, AC = 5.5
d. no, if AC=3, x is indeterminate
e. x = 1250
3. a. N = kA
b. 12 = k(100) so k = 0.12
c. N = 0.12(2500) = 300