I.EXPONENTIAL FUNCTION
A. Definition
An exponential function is a function defined by f(x) = ax , where a > 0 and a ≠ 1. The domain of the function is the set of real numbers and the range is the set of positive numbers.

B. Evaluating Exponential Functions
1. Given: f(x) = 2x, find
a. f(3) = ____b. f(5) = _____c. f(-2) = ______ d. f(-4) = ______ 2. Evaluate f(x) = ( 1)x if
2
a. x = 2 ____b. x = 4 _____c. x = -3 ______ d. x = -4 _______

C. Graphing Exponential Functions
On the same Cartesian Coordinate plane, sketch the graphs of each set of exponential function 1. a) f(x) = 2xb. f(x) = 3xc. f(x) = 4x
2. a) f(x) = 2xb. f(x) = 2x + 1c. f(x) = 2x – 1
3. a) f(x) = 2xb. f(x) = 2x + 2c. f(x) = 2x – 3
4. a) g(x) = 2- xb. g(x) = 3- xc. g(x) = 4 – x

D. The Property of Equality for Exponential Equations
Let a, b and c be real numbers and a≠ 0, then ab = ac if and only if b = c Examples:
1. 32x = 362. 23x = 83. 643x = 84. 10- x = 1/10000
5. 43x = 16x + 26. 16- x = 1/647. 93x = [ 1/3]58.5x+2 – 5x + 1 + 5x = 2625

Do as directed:
A. Evaluate:
1. If f(x) = 3x, what is
a. f( 3)?= ____ b. f( 4) = _____c. f( -2) = _____ d. f( -4) = _____ 2. What is g(x) = [ 1/3 ]x if
a.x = 2 ____ b. x = 4 ______c. x = -3 ______ d. x = -4 ______

B. Solve for x
3. 2x = 1286. 243x = 3
4. 3x = 817. 2x + 2 + 2x + 1 + 2x = 896
5. 42x = 8x + 1 8. 272x – 2 = 95 – x

C. Challenge!!!
9. If x is real and x64 = 64, what is x32?
10. Find the value of xy if 2x = 7 and 7y = 64.
11. If 183 = 2x •3y, find the integer values of x and y. 12. There are about 1,000 bacteria in a certain culture. If the amount doubles every 2 Hours, about how many bacteria would there be after 8 hours?

13. A radioactive substance is decaying (it is changing into...

...A function is a relation in which each element of the domain is paired with exactly one element in the range. Two types of functions are the exponentialfunctions and the logarithmicfunctions. Exponentialfunctions are the functions in the form of y = ax, where ''a'' is a positive real number, greater than zero and not equal to one. Logarithmic...

...Exponential and LogarithmicFunctions
* Verify that the natural logarithm function defined as an integral has the same properties as the natural logarithm function earlier defined as the inverse of the natural exponentialfunction.
Integrals of Exponential and LogarithmicFunctionsFunction | Integral |
lnx | x ∙ lnx - x + c |...

...LOGARITHMIC AND EXPONENTIALFUNCTIONS
Inverse relations
ExponentialfunctionsExponential and logarithmic equations
One logarithm
THE LOGARITHMICFUNCTION WITH BASE b is the function
y = logb x.
b is normally a number greater than 1 (although it need only be greater than 0 and not equal to 1). The function is defined for all...

...CHAPTER 1
1.1 Introduction
Exponential and logarithms functions are important concepts that play crucial roles in college mathematics courses, including calculus, differential equations, and complex analysis. The purpose of this study is to describe a theory of how students might develop their understanding of these topics and to analyze understanding of these concepts within the context of this theory, their application in real life phenomena and discussing...

...APPLICATIONS OF EXPONENTIAL|
AND|
LOGARITHMICFUNCTIONS|
EARTHQUAKE WORD PROBLEMS:
As with any word problem, the trick is convert a narrative statement or question to a mathematical statement.
Before we start, let's talk about earthquakes and how we measure their intensity.
In 1935 Charles Richter defined the magnitude of an earthquake to be
where I is the intensity of the earthquake (measured by the amplitude of a seismograph...

...MATH133 Unit 5: Exponential and LogarithmicFunctions
Individual Project Assignment: Version 2A
Show all of your work details for these calculations. Please review this Web site to see how to
type mathematics using the keyboard symbols.
IMPORTANT: See Question 1 in Problem 2 below for special IP instructions. This is
mandatory.
Problem 1: Photic Zone
Light entering water in a pond, lake, sea, or ocean will be absorbed or scattered by the particles
in...

...Solving Exponential and Logarithmic Equations
Exponential Equations (variable in exponent position)
1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e”...

...CHAPTER 2
EXPONENTIAL AND LOGARITHMS FUNCTIONS (534)
2.1 Exponentialfunctions and their graph
Definition
An exponentialfunction with base b is defined by the equation
[pic] Or [pic] ([pic] [pic]and x is a real number)
The domain of any exponentialfunction is the interval ([pic] The range is the interval [pic]
Example 1: Graph the...

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