February 9, 2012 At the end of today, you will be able to solve exponential functions. Warm-up: Evaluate without a calculator 1.arcsin HW 3.1b: Pg. 227 #45-52all, 61-63all Quiz next week! Test Corrections due tomorrow!

3.1b Solving Exponential Equations In this unit we are solving for the exponent 3 x = 3 5 x = 5 4 x+1 = 4 7 x + 1 = 7 x = 6 To solve for the exponent, they must have the same base on both sides of the equal sign.

Example 1: Solving exponential equations with the same base. Solve for x: 5 2x +10 = 5 4 2x + 10 = x = -6 x = -3 Since the bases (5) are the same, equate the exponents and solve.

Before we go to examples with different bases, let’s make a chart! Basic Powers 2 -2 = 3 -2 = 2 2 = 3 2 = 4 2 = 5 2 = 2 3 = 3 3 = 4 3 = 5 3 = 2 4 = 3 4 = 4 4 = 5 4 = 2 5 = 2 6 = /41/9

Example 2: Solving when they don’t have the same base. Solve for x: 2 x = x = 2 2(3) x = 2(3) x = 6 Since 4 can be written as 2 2, use 2 2 to get a same base. Now that they have the same base, equate the exponents.

Example 3: Base e Like π, e is an irrational number and referred to as the natural base. Its value is approximately Solve 3x = 4 3x + 1 = 5 x = 4/3

Practice time! 1.4 3x = x – 2 = = 25 x – x – 1 = e x + 2 = e 2x x = 4 x = 3 x = -4 x = 2 x = -1 x = 5 x = -9/2 x = 4, -2

Solving Compound Interest Problems After 5 years, the balance A in an account with Principal and annual interest rate r (in decimal form) is given by the following formulas. - For n compoundings per year: - For continuous compounding: Example: A total of $12,000 is invested at an interest rate of 9%. Find the balance after 5 years if it is compounded: a) quarterly b) continuously