Merced College; Don Power

 

STUDY GUIDE, CHAPTER 5

 

5.1       Graph an exponential function, possibly with a transformation:

 

            Ex:  y = 2x, ex, −ex, 3−x, 2x−3−3

 

5.2       Given an exponential function that represents compound interest, population growth, or radioactive decay, find either the initial quantity, the final quantity, or the time (if two of these three quantities are given).  To find the time, you may solve graphically with a calculator.

 

5.2       Be able to set up the compound interest formula A = P(1+r/n)nt  and solve directly or graphically for any missing variable.

 

            Ex:  5.2#5, 15, 23, 31

 

5.2       Be able to set up the exponential growth/decay formula  f(x) = Pax = P(1±r)x and solve directly or graphically for any missing variable.

 

            Ex:       5.2 #45, 51

 

5.2       Be able to set up the half-life formula for exponential decay M(x) = c(0.5x/h) and solve directly or graphically for any missing variable.

 

            Ex:  5.2 #57, 59

 

5.4A    Evaluate a log expression like  or  without a calculator.

 

5.5.  Solve a log equation (one-to-one, or requiring conversion to an exponential equation)—with or without a calculator.  It may require logs to be condensed before you can solve.

 

            Example:  Convert to exponential form and solve for x: 

 

            Example:  Solve  .  Give both an exact (non-calculator) value and a decimal approximation.  Note:  You will need to condense the log terms into a single logarithmic expression.

 

 

5.5.  Solve an exponential equation (one-to-one, or requiring conversion to a log equation)---with or without a calculator

 

            Ex:       5.5 #9-21

 

5.4.  Condense or expand a log expression.

 

            Expansion example:  Use the properties of logarithms to rewrite  as the sum and/or difference of logarithms

 

54A.  Use the change of base theorem and the calculator to evaluate an expression like

 

            Ex:  Find the value of log543 using a calculator.  Briefly describe how you got your result.  Show how to check the result on the calculator

 

5.1, 5.3            Graph an exponential or a log equation.

 

 

 

NOT TO BE ON THIS TEST: 

 

1.  Given a table of values, find a exponential regression equation (or a natural log regression equation).  Based on the regression equation predict (forecast) a new value.

 

 

2.  Using the following data:

 

x

2

4

6

8

 

 

y

5.84

11.61

29.04

61.37

 

            a.  Which model gives a better fit, linear regression, exponential regression, or logarithmic                         regression?  Explain why you chose your answer (use the computed correlation).

            b.  Using the best type of regression, forecast y when x = 10.

            c.  Write the regression equation.

 

3.  Use your calculator to solve a word problem involving compound interest (periodic compounding or continuous compounding), the future value of an annuity (used for saving plans), or the present value of an annuity (used for loan payments).  I will give your all four formulas;  you will have to decide which formula to use, show the substitutions into the formula, and the calculator solution (I recommend the SOLVER for these, but you can also graph and find the root).  Examples:  Lesson 4.5, #9, 13, 17, 37, 39, 41, 43

 

 

 

 

 

 

Return to:  Merced College; Don Power               Updated 11/01/05 by Don Power