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Notes for a mathematics class on exponential functions, including an introduction to the concept and a comparison of two payment options. Students are asked to determine formulas for each option, calculate the amount of money received for attending a certain number of classes, and graph the money made over 30 classes. The document also reviews laws of exponents and properties of exponential functions.
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MATH 1113 PreCalculus Section 5.3 notes
Introduction to Exponential functions
Suppose that are dreaming and I offer to pay you each day for attending class! Being even more generous in
dreamland, I offer you a choice:
Choice 1 – Receive $1,000 per class attended. Choice 2 – Receive 2 cents on the first day you attend class,
4 cents the second day, 8 cents the third day, and so on.
Before we go on, which choice do you choose? _____
a) 10 classes ________________________
b) 20 classes ________________________
c) 30 classes ________________________
classes.
y
x
Class Amount received Formula? 0 1 2 cents 2 4 cents 3 8 cents 4 5... x
a) 10 classes _______________________
a) 20 classes ______________________
b) 30 classes _______________________
x
If s, t, a, and b are real numbers, with a > 0 and b > 0, then
0 =
− a a
a
a a a ab
s s s
s t st s
1 2 4 _____________ 2. − =
13 ( 27 ) _______________ 3. =
3 6 1 3 ( x y ) ___________
For more review of these rules see the appendix A pages A85-A87.
The exponential function f with base a is ________________, where a > 0 and a ≠ 1.
Consider x f ( x )= 3 , x g ( x )= 7 ,
x h x
( ) , and
x r x
x f ( x )= a
Graph
x
x
x
f x e
f x
f x
A Property of Exponential functions a^ a u v
u v If = ,then =
Use the above property to solve the following equations:
x −
x x 4 2
2 = 3) 4 2
1
1
^ =
− x
5.3 Assignment 1-10ALL, 11, 17, 21, 23, 29-36ALL, 37-40ALL, 45-48ALL, 53-75ODD
3 - Solve: 2 32 x =
( )
2 1 4 3
1 Solve: x x e (^) x e e
− − = ⋅