Lesson+Summaries+-+Exp+Functions

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 * Logs and Exponents **
 * Emily Brant **
 * April 18,2011 **

(xa)(xb) = xa+b (xa)b = xab xa = xa-b xb x0 = 1 x-a = 1 xa
 * Rules (Exponents) **

loga+logb = logab logan = nloga logsab = c base exponent ac = b change of base loga = loga logb
 * Rules (Logs) **

· The rate of change (or derivative) of an exponential function is also exponential · F(x0 = ____x where the derivative and function are the same  · _____ is ~2.7182 … between 2.5 and 3, also known as ** e (euler’s #) **   · ** e ** is the derivative of itself, therefore meaning: the derivative of ** e ** is ** e **   · y=e à   y’=e
 * Derivative of an exponential function **

= = =April 20th - The Natural Logarithm= =By Moe Qureshi=

For more info on the natural logarithm visit: http://mathworld.wolfram.com/NaturalLogarithm.html http://en.wikipedia.org/wiki/Natural_logarithm

__Natural Exponential and Logarithmic Functions:__ Tuesday, April 26, 2011. By: Arlanna Pugh **Overview:** Today in class we had the opportunity to watch one of Gillian's favourite math movies (starring Daffy Duck). After viewing the short film we participated in a Derivative Activity with a partner where we had to determine which rules were suitable for each question and then had to solve it accordingly (4 questions total). **In-Class Worksheet:** Derivatives of the Natural Exponential and Logarithmic Functions Answers were taken up in class. **In-Class Homework:** Differentiating Exponential Functions Homework Both answers to the two questions were required to be checked by Gillian **Question #1**: Identify any local extrema for the function: y = (x^4)(e^x) Steps for solution: Answer #1: Local Min at (0,0); Local Max at (-4, 4.7) **Question #2:** A motorcycle cost $10,000, but its value depreciates over time. The value can be modeled by: V(t) = 10000(e^-t/4), where V is the value of the motorcycle after t years. V'(t) = -2500 (e^-t/4) V'(0) = -2500 (e^-0/4); therefore -$2500/ year 1/4 x $10000 = $2500 <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0in; margin-left: 0.323in; margin-top: 0in; margin: 0in; unicode-bidi: embed;">2500 = 10000(e^-t/4) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0in; margin-left: 0.323in; margin-top: 0in; margin: 0in; unicode-bidi: embed;">t = 5.5 years <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0in; margin-left: 0.323in; margin-top: 0in; margin: 0in; unicode-bidi: embed;">__Tonight's Homework:__
 * 1) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0px; margin-left: 0.375in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">Solve for the first derivative
 * 2) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0px; margin-left: 0.375in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">Set the first derivative to 0
 * 3) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0px; margin-left: 0.375in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">Solve for x
 * 4) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0px; margin-left: 0.375in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">Sub x values into the original function and solve for y
 * 1) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0px; margin-left: 0.323in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">Rate of Change Expression:
 * 1) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0px; margin-left: 0.323in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">Rate that the value of the motorcycle was depreciating at when purchased:
 * 1) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; margin-bottom: 0px; margin-left: 0.323in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">When to sell bike when it is worth 1/4 of purchase price:
 * 1) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; list-style-type: disc; margin-bottom: 0px; margin-left: 0.323in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">Review Natural Exponential and Logarithmic Functions
 * 2) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; list-style-type: disc; margin-bottom: 0px; margin-left: 0.323in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">Practice review questions will be handed out tomorrow
 * 3) <span style="direction: ltr; font-family: Calibri; font-size: 11pt; list-style-type: disc; margin-bottom: 0px; margin-left: 0.323in; margin-top: 0px; unicode-bidi: embed; vertical-align: middle;">**QUEST: Friday, April 29, 2011.**

** Talha Sadiq ** ** April 27, 2011 ** ** Work Period **

Today was a work period and we got time in class to work on the practice quest and a review sheet on Exponential and Logarithmic Functions. The quest on this chapter is on __**Friday, April 29, 2011**__. Here are some links that would help you review for the test! Good Luck!

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** Homework: ** Complete the review sheet & practice quest! Review for the quest this friday!

Jane Yang Today we had our Logs and Exponential functions Quest
 * April 29, 2011**