L04 - t years 6 Suppose you invest $1000 in an account that...

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L4 – Exponential Functions Def – A function of the form f ( x ) = a x where a is a positive constant is called an exponential function. Further, 1. If x = n , a positive integer, then 2. If x = 0, then 3. If x = - n , then 4. If x is a rational number, x = p q , where p and q are integers and q > 0, then 1
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5. If x is an irrational number, then to make f ( x ) a smooth curve with no gaps for x any real number: 2
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Graphs: 3
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Laws of Exponents 1. a x + y 2. a x - y 3. ( a x ) y 4. ( ab ) x 4
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Sketch the graph of y = 3 - x - 1 y = 2 x - 1 + 3 5
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Application: The half-life of Strontium-90 is 25 years. In a sample of 80 mg, find an expression for m ( t ), the amount remaining after
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Unformatted text preview: t years. 6 Suppose you invest $1000 in an account that doubles every 6 years. What will the value of the account be in 24 years? Estimate the value in t years. 7 Consider the function f ( x ) = a x for different values of a . If a = 2, If a = 3, For what a would the slope of the tangent line at x = 0 be 1? 8 Def – e is the number such that Properties Sketch the graphs of y = e x and y = e-x . Sketch y = 2 e-x . 9 Sketch the graphs of y = 1-e x and y = e-x + 2. 10...
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This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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L04 - t years 6 Suppose you invest $1000 in an account that...

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