Practice Exam 2

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Key

Problem 1  

Use your calculator to find log₃29 rounded to three decimal places.

Problem 2

Solve for x:   ln(x + 1) + ln(x + 2)  =  3

Problem 3

The number of grams N of C₁₄ left in a fossil after t years is 

N = 0.03e^-.000121t 

A fossil has been analyzed and found to contain 0.0002 grams.  How old is the fossil?

Problem 4

Solve the following equations

A. 

B.  (3x - 2)² +9(3x - 2)  =  -20

Problem 5

Solve the following nonlinear system of equations

         2x² - 3y²  =  29
         x² + y²  =  17

Problem 6

Use the graphs below to solve the following nonlinear system

        x² + y⁴  =  1
        x + y = 3

Problem 7

Solve the inequalities

A.  x² + 3x - 4 < 0

B.    x-2
                    >   2
        x-5

Problem 8 

The graph of the function 

                  x² + x +  4
       y  =                              
                      x - 2

is shown below.  Use the graph to solve the inequality

             x² + x +  4
                                < 0    
                 x - 2

Problem 9

Sketch the graph of the circle with equation 

        x² + y² + 4x - 6y  =  3

Problem 10

Find the equation of the parabola that opens downward, has vertex (1,3) and passes through the point (2,1).