1) Solve the following equations algebraically. You must show all your work.

a) t^2/3 = 4       

b) ⁵√(x+1) = 3

c) (2/3) = 2 - (5x - 3) / (x - 1)

2) Solve algebraically and check your potential solutions: √(t + 12) - t = 0

3) The volume of a cube is given by V = s³, where s is the length of a side. Find the length of a side of a cube if the volume is 700 in³. Round the answer to three decimal places.

4) a) Show the steps that you would take to solve the following algebraically: (3 / (x - 3)) = (x / (x - 3)) - (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) = 1.3x / (100 - x)

a) 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 = √(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.

c) Graph in MS Excel or another web-based graphing utility and paste your graph here.

7) Suppose that N= √x + 4models the number of cases of an infection, in millions, of a disease x years from now.

a) Approximately how many cases of the infection will there be 16 years from now?

b) In approximately how many years will there be 6 million cases?