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appendix D- mosquitoes mat 117

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Axia College Material
Appendix D
Health
Millions of people around the world either do not have access to natural water sources or do not have the
means to clean and purify the water sources they do have. Charitable organizations have been
established to build water filtration systems in order to provide drinkable water in the areas of need.
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
x2200
000,5
C
=
a. What is the cost to remove 50% of the pollutant?
In order to find out the cost we just replace x=50 in the model equation. So:
C=
5000
2002 ×50
=
5000
100
=50
million dollars
b. What is the cost to remove 75% of the pollutant?
In order to find out the cost we just replace x=75 in the model equation. So:
C=
5000
2002 ×75
=
5000
50
=100
million dollars
c. What is the cost to remove 99% of the pollutant?
In order to find out the cost we just replace x=99 in the model equation. So:
C=
5000
2002 ×99
=
5000
2
=2500
million dollars
d. For what value is this equation undefined?
The equation is undefined when the denominator equals 0. So:
200-2x=0 2x=200 x=100
In other words the cost for removing 100% of pollution in a lake is undefined.
e. Looking at your answers in ‘a’ through ‘d’ what can you say about cost versus percent of
pollution that can be removed from a lake?
As you are looking at the answers from ‘a’ through ‘d’ you can see that as the percent of
pollution increases, so does the cost to remove it. Moreover, the cost for removing 100%
pollution is undefined because it is impossible to do such thing.
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Busch Enteratinment Corporation. (N.D.). Flamingos. Retrieved from
http://www.seaworld.org/animal-info/info-books/flamingo/physical-characteristics.htm
2. Doctors want to set up a station to vaccinate the people against measles. Suppose that the costs
for such a station are $1,500 for setup costs and $3.00 to administer each shot.
a. Write an expression that gives the total cost of vaccinating x people.
The total cost to vaccinate x people can be expressed as:
1500+3x
b. You can find the average cost per person by dividing total costs by number of people.
Write the expression that gives the average cost per person.
The average cost per person can be expressed as:
C=
1500+3x
x
c. Find the average cost per person for 10 people, 100 people, and 1,000 people.
We now solve the above expression for the three different values of x.
For 10 people:
C=
1500+3 × 10
10
=
1530
10
=153 dollars
For 100 people:
C=
1500+3 × 100
100
=
1800
100
=18 dollars
For 1000 people:
C=
1500+3 × 1000
1000
=
4500
1000
=4.5 dollars
d. As the number of people given the shot increases, what happens to the average cost to
vaccinate each person? Would the average cost ever fall below $3.00? If so, identify a
value that supports your answer. If not, explain how you know.
If we write the average equation in another form we can easily see that the average cost
could never fall below $3. Also this form of the equation clearly shows that the cost
decreases as the number of people vaccinated increases. So by splitting the rational
expression in the equation we get the following form of the average cost equation:
e. How many people need to be vaccinated for the average cost to be $5.00 per person?
In order to find out we need to solve the equation for x when C=5. So:
5=
1500+3x
x
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5x=1500+3x 5x-3x=1500 2x=1500 x=750 people
So for 750 people vaccinated, the average cost would be 5 dollars.
3. To estimate the mosquito population, biologists count the total number of mosquitoes in a small
section of the lake. The total population of mosquitoes 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.
If we denote m-the number of mosquitoes and s-the size of the habitat, then the equation
would be:
m=k×s
b. A biologist counted 1200 mosquitoes in a 10-acre parcel of the lake. Find the constant of
variation k.
In order to find out we solve the equation for k when m=1200 and s=10:
1200=k×10 k=
1200
10
= 120
c. If the entire lake is 2,500 acres, then what is the total mosquito population Describe how
you arrived at your answer.
In order to find out we solve the equation on point a. for m when s=2500 and k=120. This
way we can find the total mosquito population:
m=120×2500 m=300,000 mosquitoes
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Really great stuff, couldn't ask for more.

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