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Study fact sheet test 3

# Study fact sheet test 3 - Growth Rate The rate at which it...

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Jake Venditto 10/26/09 Groom Study Fact Sheet Chapter 3.1 – 3.4 Exponential Function vs. Linear Function Linear growth continues to increase or decrease at a constant rate, whereas exponential growth increases or decreases at an expanding rate. Exponential X 1 2 3 4 5 6 F(X) 2 4 8 16 32 64 Linear X 1 2 3 4 5 6 F(X) 2 4 6 8 10 12 Linear Exponential Linear and Exponential Formulas from Word Problems The Number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let N represent the number of asthma sufferers (in millions) world wide t years after 1990. Linear: ∆Y 130 – 84 = 46 slope = 4.18 ∆ X 2001 – 1990 11 N(t) = 4.18t + 84 Exponential: N(t) = 84b 130 = 84b N(t) = 84(1 + .0405) N(t) = 84(1.0405) Increases by 4.05% each year B = 1.0405 Drawn Conclusions: How many asthma sufferers are predicted worldwide in the year 2010? Linear: Nikki stinks(t) = 4.18(20) + 84 Exponential: N(t) = 84(1.0405) N(t) = 167.64 million N(t) = 185.832 million

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Growth Factor : Y = a b The Growth factor (b) is 1 + the growth rate

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Unformatted text preview: Growth Rate : The rate(%) at which it grows or decays B = 1 + the rate(%) Graphical Effects of a and b in the form y = a(b) A – where the graph intersect the y-axis B – the rate at which it grows or decays, steep or gradual Ex. Writing Linear and Exponential Formulas from Given Points Given the points (2, 6) and (4, 96) Write the linear and exponential equations of the functions which pass through those points Linear: Exponential: x Y = 7(.5) Y = 3(1.5) Writing Linear and Exponential Formulas from a Table of Values X 2 4 6 8 10 F(x) 2 4 8 16 32 64 Linear: Exponential: Definitions of “e” 1. e = lim (1 + x ) x 2. e = lim ( 1 + (1/x)) x ∞ Constant Rate of Change : Linear y = mx + b m = rate of change 1/x x Percent Rate of Change: Exponential y = ab b = 1 + the rate of change Continuous Rate of Change Exponential y = ae k = continuous rate e = growth factor x kx k...
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