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By Thersia Weber and Rachel Eron

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f(x) = ab x a = initial amount b = rate of growth/base x = variable b > 1: exponential growth b < 1: exponential decay Only an exponential function if the x is in the exponent.

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f(x) = 3 x Exponential Function? Initial Value? Base? Growth or Decay? Yes X is in exponent 1 A isn’t listed, automatically 1 3 B=3 Growth B=3 > 1 f(x) = 4x 7 Exponential Function? Initial Value? Base? Growth or Decay? No X isn’t in exponent - - -

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x f(x) -296 -124 06 13/2 23/8 Power a = x = 0 then plug it into y=ab x y=6b x then plug in another value on the table 3/2 = 6b 1 solve for b b= 3. 1 2 6 b= 3 = 1 12 4 plug b into equation y= 6(1/4) x

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x f(x) -2108 -136 012 14 24/3 x f(x) y = 12 (1/3) x 19004.8 19105.6 19206.5 19307.6 19407.9 19508.7 196010.1 197011.1 y = 4.8 e.0154x y = ab x y = 12b x 4 = 12b 1 4/12 = b 4/12 = 1/3 = b y = 12 (1/3) x y = ab x y = 4.8b x 5.6 = 4.8b 10 1.167 = b 10 ln 1.167 = 10 ln b ln b =.0154 b = e.0154 y = 4.8 e.0154x

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http://www.explorelearning.com/index.cfm?method=cR esource.dspView&ResourceID=104# Graph transformations previously learned also apply to exponential functions Horizontal Translations y = ab x-c graph shifts to right y = ab x+c graph shifts to left Vertical Translations y = ab x +c graph shifts up y = ab x -c graph shifts down Axis Flips y = ab -x graph flips over y axis y = -ab x graph flips over x axis Use URL to explore transformations of Exponential functions on graph

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The number B of bacteria in a petri dish culture of t hours is given by: B = 100e 0.693t Find initial number of bacteria present. How many bacteria are present after 6 hours? Exponential equations can be found in many real life situations. To solve real life equations, look at it as y = ab x and find initial amount and other variables. Plug in the numbers given and find the information asked for in problem. Initial: 100 # Present after 6 hours: 6394 B = 100e 0.693t B = 100e 0.693x6 B = 6394

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Suppose your parents are going to pay you a weekly allowance for doing your household chores this coming year. Also, imagine that they are going to give you a choice of two payment schemes. With Choice A, your parents will pay you $10 every week. Therefore, you will have earned $10 after the first week, $20 after the second week, $30 after the third week, and so on. With Choice B, just to be nice, they are going to pay you $0.01 before you even start working. After you complete chores for week one, they will double your money, thus giving you a total of $0.02. After you complete chores for week two, they will once again double your money, thus giving you a total of $0.04. They will continue to double your money at the end of every week. Write an equation for each payment scheme and use www.graphsketch.com to make graphs. Explain which payment scheme you will choose and why using the graphs. www.graphsketch.com Each project will be turned in and graded according to rubric, worth 20 points.rubric

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Each payment scheme will give you a fair amount of allowance, but judging by the graphs, the second payment plan would be a better choice because you will earn more eventually, faster. 2-3 groups to present explanation. If present, 5 extra credit points.

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Precalculus Textbook by Franklin Demana, Bert Waits, Bregory Foley, and Daniel Kennedy www.graphsketch.com (Graph, slide 10) www.graphsketch.com http://www.explorelearning.com/index.cfm? method=cResource.dspView&ResourceID=10 4# (Graphing Activity, slide 7) http://www.explorelearning.com/index.cfm? method=cResource.dspView&ResourceID=10 4# http://www.cartoonstock.com/directory/e/ex ponential_growth.asp (Introduction Comic) http://www.cartoonstock.com/directory/e/ex ponential_growth.asp http://education.ti.com/calculators/downloa ds/US/Activities/Detail?id=7727 (Supplemental Activity, Allowance) http://education.ti.com/calculators/downloa ds/US/Activities/Detail?id=7727

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Now take a 10 question assessment on what you’ve learned. Assessment Assessment Assessment Answers Assessment Answers

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