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by: Mary Veum

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# Calculus Ia MATH 1125

Mary Veum
UCONN
GPA 3.97

Erin Mullen

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COURSE
PROF.
Erin Mullen
TYPE
Class Notes
PAGES
3
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 3 page Class Notes was uploaded by Mary Veum on Thursday September 17, 2015. The Class Notes belongs to MATH 1125 at University of Connecticut taught by Erin Mullen in Fall. Since its upload, it has received 8 views. For similar materials see /class/205820/math-1125-university-of-connecticut in Mathematics (M) at University of Connecticut.

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Date Created: 09/17/15
Section 15 Section 15 Exponential Functions An exponential function can be written in the form y f 96 am where a is a positive constant What does this mean Consider the following cases 0 z n Where n is a positive integer o z 0 o z in Where n is a positive integer o z 2 Where p and q are integers q gt 0 this is a rational number 0 z is an irrational number ie not rational Graphs of Exponential Functions oagt1 00ltalt1 Section 15 2 Example 1 Graph the following exponential function using transformations and state the domain and range we 2 e 4 1 Laws of Exponents If a and b are positive numbers and z and y are any real numbers7 1 aHy away m 2 aH CL ay 3 aw aw Cay 4 abw ambw 5 am ay ltgt z y NonLaws of Exponents 1 aHy 31 1m ay 2 abm 31 ab 3 a bm 7 am b So f 2 7 4 m 2 7 and g 2m 2w2 2 if but h 32m 31 6w Example 2 Simplify the following expression so that it is written as a constant times a power of x Example 3 Solve the equation 2 16w 8 1 for x Section 15 Example 4 A culture of 200 bacteria triples in size every 2 hours a What is the size of the culture after 6 hours b What is the size of the culture after t hours c Graph the population function and estimate the time for the population to reach 50000 The Numb er 6 De nition The number 6 has a variety of de nitions depending on which point of View you7d like to take and what knowledge is assumed For now we de ne e to be the constant so that the exponential function fz em has a tangent line with slope 1 at the point 01 It turns out that e 271828 Example 5 Starting with the graph of y em nd the equation of the graph that results from re ecting about the line z 72

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