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By Thersia Weber and Rachel Eron. f(x) = ab x a = initial amount b = rate of growth/base x = variable b > 1: exponential growth b < 1: exponential decay.

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Presentation on theme: "By Thersia Weber and Rachel Eron. f(x) = ab x a = initial amount b = rate of growth/base x = variable b > 1: exponential growth b < 1: exponential decay."— Presentation transcript:

1 By Thersia Weber and Rachel Eron

2

3 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.

4 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 - - -

5 x f(x) /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= b= 3 = plug b into equation y= 6(1/4) x

6 x f(x) /3 x f(x) y = 12 (1/3) x 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 = b 10 ln = 10 ln b ln b =.0154 b = e.0154 y = 4.8 e.0154x

7 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

8 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

9  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 to make graphs. Explain which payment scheme you will choose and why using the graphs.  Each project will be turned in and graded according to rubric, worth 20 points.rubric

10  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.

11  Precalculus Textbook by Franklin Demana, Bert Waits, Bregory Foley, and Daniel Kennedy  (Graph, slide 10)  method=cResource.dspView&ResourceID=10 4# (Graphing Activity, slide 7) method=cResource.dspView&ResourceID=10 4#  ponential_growth.asp (Introduction Comic) ponential_growth.asp  ds/US/Activities/Detail?id=7727 (Supplemental Activity, Allowance) ds/US/Activities/Detail?id=7727

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


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