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Study Fact sheet 4

# Study Fact sheet 4 - its size Ex The population of rabbits...

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Jake Venditto 11/8/09 Groom Study Fact Sheet Chapter 4.1 – 4.3 Change of Base Formula Example 1: Example 2: Converting Exponential form to log form 1. Convert to logarithmic form: 8 = 2 x The exponent is the answer The Base is constant x = log 2 8 2. Convert to exponential form: y = log 3 5 The answer is the exponent The Base is constant 3 y = 5 log b 1 = 0 log b b = 1 log b b 2 = 2 log b b x = x b log b x = x log a b = 1/log b a Properties of Logs log b ( xy ) = log b x + log b y log b ( x/y ) = log b x - log b y log b ( x n ) = n log b x log b x = log a x / log a b

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Domain and Range of Ln and Log Graphs Natural Log Graphs Common Log Graphs Y = 2 ln(X – 3) Y = 2 Log X Domain: Domain: X > 0 X > 3 Range: R Modeling Logs through Word Problems In the formula, A represents the amount of money that will be in the account when \$1200 is doubled. P represents principal - the amount of money currently being invested. The letter r stands for rate of interest, and t stands time in years. Doubling Time Doubling time is the amount of time it takes for an increasing exponential to grow twice

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Unformatted text preview: its size Ex. The population of rabbits grows according to the function R(t) = 200(1.53) , where t is measured in years. Find the time it would take for a population of 200 rabbits to double in size. Half-Life: Half-life is the amount of time it takes for a decreasing exponential function to reduce to half of its previous size. Ex. The half-life of a particular substance ABC is 10 hours. Today you have 30 grams of the substance ABC. Find an equation that gives the amount of substance ABC remaining after t hours. Use this equation to determine the number of hours needed for the substance to decay to 5 grams. Converting between Y = ab and Y = ae From y = ab to y = ae b = growth facter, 1 + rate, e Ex. Y = 5(1.2) b = 1.2 Rate = .2 e = .2 k = .1823 Y = 5e From y = ae to y = ab Ex. Y = 3e K = .123 e = 1.13 = b y = 3(1.13) Solving Equations with ln and e Ex. e - 6e + 5 = 0 Ex. (ln x) - 6(ln x) = 7...
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