Radical Functions and Word Problems

Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all your work.

(You may type cuberoots as cbrt(x) and show raising to the nth power as ^n, like x^3.)

Find x:
a) (1/4) = 3 - (2x-1)/(x+2)
b) x^(2/3) = 125
c) cbrt(x) - 4 = 2

2) Solve algebraically and check your potential solutions (if a potential solution is not valid, then show why and explain): sqrt(x + 20) - x = 0

3 a) Show the steps that you would take to solve the following algebraically: 4- x/(x-2) = -2/(x-2)

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

4) The following function computes the cost, C (in millions of dollars), of implementing a city recycling project when x percent of the citizens participate. C(x) = 1.4x/100 - x

a) Using this model, find the cost (in millions of dollars) if 60% of the citizens participate? (In this problem, it is not necessary to change x, the percentage, to its decimal equivalent before using it in the problem.)

b) Using this model, determine the percentage of participation that can be expected if $4 million is spent on this recycling project. Set up an equation and solve algebraically. Round to the nearest whole percent.

5) 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 500 cm3. Round answer to three decimal places.

6) Suppose that N= sqrt(x) + 3 models the number of cases of an infection, in millions, of a disease x years from now.

a) How many cases of the infection will there be 9 years from now?

b) In how many years will there be 5 million cases?

7) a) If y= sqrt(x) - 2 , fill in the following table for x = 0,1,2,3,4. Round to three decimal places where necessary.

x y
0
1
2
3
4

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

c) Graph it in MS Excel or another web-based graphing utility.