PreCalculus: Lesson Plan * 10/27/2006

Quickstart
Block I
p.245 #96
Human Memory Model

Lesson
3.4 Solving Exponential and Logarithmic Equations
Objectives: Students will know how to solve exponential and logarithmic equations.

I. Introduction and Review (p.247)
A. One-to-One Properties
a^x = a^y if and only if x = y
log_ax = log_ay if and only if x = y.
B. Inverse Properties
log_aa^x = x
a^log_ax = x

II. Solving Exponential Equations (pp. 249 - 249)
Two very general keys to solving exponential equations are:
1. Isolate the exponential expression
2. Use the second one-to-one property from above.
See Examples 3, 4, 5

IV. Application
See Example 12 in textbook about Doubling an Investment
Example 5: Saving for Retirement
You have $50,000 to invest. You need to have $350,000 to retire in thirty years. At what continuously compounded interest rate would you need to invest to reach your goal?
A = Pe^rt
350,000 = 50,000 e^30r
7 = e^30r
ln 7 = ln e^30r
ln 7 = 30r
r = ln 7 / 30 ≈ 6.5%

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