1. Solve the following equations algebraically. You must show all your work.
   Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may type \[\sqrt[3]{x}\] as cuberoot ( x ) and show raising to the n th power as ^ n , like x ³ is typed x ^3.
   1. \[{{t}^{\frac{2}{3}}}=4\]
      

3) The volume of a cube is given by V = s ³ , where s is the length of a side. Find the length of a side of a cube if the volume is 700 in ³ . Round the answer to three decimal places.

4) a) Show the steps that you would take to solve the following algebraically: \[\frac{3}{x-3}=\frac{x}{x-3}-\frac{3}{2}\]

b) What potential solution did you obtain? Explain why this is not a solution.

5) For the following function, C computes the cost in millions of dollars of implementing a city recycling project when x percent of the citizens participate. \[C(x)=\frac{1.3x}{100-x}\]

1. Using this model, approximately what is the cost if 40% of the citizens participate? Include units with your answer.

b) Using this model, estimate the percentage of participation that can be excepted if $3 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.

6) a) If \[y=\sqrt{x}-1\] , fill in the following table for x = 0, 1, 2, 3, 4. Round to three decimal places where necessary.

b) Explain why no negative values are chosen as values to substitute in for x .

1. Graph in MS Excel or another web-based graphing utility and paste your graph here.
   7) Suppose that N = \[\sqrt{x}+4\] models the number of cases of an infection, in millions, of a disease x years from now.
   1. Approximately how many cases of the infection will there be 16 years from now?
      
   2. In approximately how many years will there be 6 million cases?

8) also typed as D=sqrt(2h), can be used to approximate the distance, D, in miles that a person can see to the horizon from a height, h, in feet. Suppose that you are in an airplane. By choosing any height, find the corresponding distance that you should be able to see to the horizon. Include the height and the calculations needed to find the distance. Include units with your answer, and show all work for full credit.

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Solution: The downloadable solution consists of 8 pages, 602 words and 2 charts.
Deliverable: Word Document