A+ Answers

1.  (10 points)

(a) Find all solutions to the equation:  x - 7 + 12 = 0.  Check your solutions

(b) Find all solutions to the equation:  section 5.5 #2.  Check your solutions.

(b)  In addition, sketch the graph of the function

y = 2x²  - 5x + 1 using the roots you found in part a and the vertex

3.     (15 points)  Find the asymptotes, the intercepts and sketch the following functions.  A computer sketch is not sufficient.  You must explain.

(a)   Section 6.2 #4.

4.     (10 points)  A rain gutter is to be made up of rectangular aluminum sheets 12 inches wide by turning up the sides edges 90 degrees.  What depth (of the edges) will provide a maximum cross sectional area and thereby provide for the greatest flow of water?

5.     (10 points)  Section 7.1 exercise number 2.

6.     (10 points)  Suppose you deposited $5000 in a savings account with an annual rate of interest of 3% compounded continuously.  How much money will be in the account in 10 years?

Solution:

7.     (10 points)

(a)   Express  in exponential form.

(c)  Determine the exact value of   ln e⁵. (Do not give a calculator estimate.)

Answer: 5

   Before you do number 8 study the following example 

Example.  (Example 2 of section 7.3 revisited)

      A person deposits $1,000 in a bank account which pays 8% annual interest compounded continuously.  How many years will it take for the amount of money in the account to double.

8.   (10 points)  A person deposits $3,000 in a bank account which pays 3% annual interest compounded continuously.  How many years will it take for the amount of money in the account to double.  Use the above process to determine an exact solution and the check your solution using the estimate of the “law of 72”.

9) (10 points)  A lake is formed with a newly constructed dam.  It is stocked with1,000 fish.  The fish population is expected to increase according to the formula

  Bonus questions

a)     Section 7.2 number 4.

b)     Simplify the following:

                           i.          Give a sketch of the graph of the function V(t).  Your graph can be a “rough draft”.

                         ii.          Determine the value of the fax machine in years 0, 1 and 4. to the nearest tenth.

                       iii.          Assume that the company decides to replace the machine when the machines values reduces to $500. In how many years will the machine be replaced?