Exponential Functions Simplified
"Learn how to simplify exponential functions, rationalize denominators, and solve equations. Understand the characteristics of exponential functions and the natural base 'e.' Find the approximate values and graph exponential functions to enhance your understanding. Explore the basics of exponential functions in this comprehensive guide."
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Presentation Transcript
Check up Simplify Completely the following: ( )5-3 7 ( ) 7-2 7 1) ( ) ( ) 6+2 6-2 2)
Check up 2 Rationalize the Denominator 5 2 3) 8 4) 5+2
Check up 3 Solve the equation: 5) 3? 3? + 7 = 5 1 3+ 5 = 8 6) 3? 6
Chapter 9 Section 1 Exponential Functions Page 662
Definitions Exponential Function f with base b f(x) = or y = Where b is a positive constant other than 1 (b > 0 and b 1) and x is any read number bx bx Example: f x ( )=2x g x ( )=10x Note: Variable is an exponent.
Simple Definition Exponential Function has a exponent as a fraction. Note: Exponent ial Function has the word, exponent .
Evaluate an Exponential Function f x ( )=42.2 1.56 ( ) 4 Evaluate: Solution: What is available for you to evaluate? Calculator Problems? Go ahead and find the value of f(x)
Find the approximate value 23.4 1) 3 5 2) e3.4 3)
Graphing Exponential Functions Set up a table of values Graph: f x ( )=2x
f x ( )=2x Graph: Table: f (x) = 2? x 0 1 1 2 2 4 Enough values to find the shape of the graph ?
Characteristics of Exponential Functions f x ( )=bx Page 666
The Natural Base e An irrational number, symbolized by the letter, e, appears as a base in many applied exponential function. The number e is defined as the value that approaches as n get larger and larger. n 1+1 n The approximate value of e is e = 2.718281827 Function, is called the natural exponential function. e is called the natural base. f x ( )=ex
Example Evaluate: a) f(x) = 1145?0.025? for x = 36
Compound Interest ( ) t A=P 1+r * P: principal, t years at interest rate r , compounded annually Semi annual, quarterly n compounding periods per year: nt A =P 1+r n A=Pert Continuous compounding:
Investment 1) Find the values of $500 after 10 years, interest rate 6.5% compounded semiannually. 2) Same amount, time, rate but compounded continuously.
Summary Definition of Exponential function.. Find approximate value of an exponential function. Graph the exponential function. Natural base e Interest formulas Compound continuously
