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

Write

       2 log_q (5x)  - log_q (3x - 2) as a single logarithm

Problem 5

Expand the logarithm 

                  25 x¹⁰ 
        log₅                    
                    y¹²

as much as possible and simplify.

Problem 6

A. Find the equation of the conic shown below

B.    Sketch the graph of the conic with the equation below:

             9y²   -   x²   =  36

Problem 7

Solve the following nonlinear system of equations

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

Problem 8 

A.  Find the indicated unknown

        8, 13, 18, 23, ..., 88            n  =  ?

B.  If the second term of a geometric sequence is -2/3 and the third term is 1/3, find a₁ and r.

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).

Problem 11

Lake Tahoe Community College had 4200 students in 2002, and has had a enrollment decline of 150 students each year since 2002. 

A.  Find the enrollment for each of five years, beginning with 2002.

B.  Find the general term a_n of this sequence.