# Exponential Functions and Models (27 pages)

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## Exponential Functions and Models

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- Pages:
- 27
- School:
- LeTourneau University
- Course:
- Math 1203 - College Algebra w/ Apps

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Exponential Functions and Models Lesson 5 3 Contrast Linear Functions Exponential Functions Change at a constant rate Rate of change slope is a constant Change at a changing rate Change at a constant percent rate Definition An exponential function x f x C a Note the variable is in the exponent The base is a C is the coefficient also considered the initial value when x 0 Explore Exponentials Given f 1 3 for each unit increase in x the output is multiplied by 1 5 Determine the exponential function x f x C a x f x 1 0 75 2 3 4 Explore Exponentials Graph these exponentials f x 2 1 1 x g x 4 0 9 x What do you think the coefficient C and the base a do to the appearance of the graphs Contrast Linear vs Exponential Suppose you have a choice of two different jobs at graduation Start at 30 000 with a 6 per year increase Start at 40 000 with 1200 per year raise Which One should you choose is linear growth One is exponential growth Which Job How do we get each next value for Option A When is Option A better When is Option B better Rate of increase a constant 1200 Rate of increase changing Percent of increase is a constant Ratio of successive years is 1 06 Year Option A Option B 1 30 000 40 000 2 31 800 41 200 3 33 708 42 400 4 35 730 43 600 5 37 874 44 800 6 40 147 46 000 7 42 556 47 200 8 45 109 48 400 9 47 815 49 600 10 50 684 50 800 11 53 725 52 000 12 56 949 53 200 13 60 366 54 400 14 63 988 55 600 Example Consider a savings account with compounded yearly income You have 100 in the account You receive 5 annual interest At end of year View comple ted table Amount of interest earned New balance in account 1 100 0 05 5 00 105 00 2 105 0 05 5 25 110 25 3 110 25 0 05 5 51 115 76 4 5 Compounded Interest Completed table Compounded Interest Table of results from calculator Set Y screen y1 x 100 1 05 x Choose Table Y Graph of results Assignment A Lesson 5 3A Page 415 Exercises 1 57 EOO Compound Interest Consider an amount A0 of money deposited in an account Pays annual rate of

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