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Unformatted text preview: A e k ( t + T ) = 1 2 A e kt , giving that e kT = 1 2 , implying e k = ( 1 2 ) 1 /T . Thus, equation (1) becomes y ( t ) = A e kt = A (e k ) t = A × p ( 1 2 ) 1 /T P t = A × ( 1 2 ) t/T , which is precisely the formula we obtain in class. Similarly, if the value of a stock portfolio (or a home) is doubled every T years, then its future value y ( t ) in t years is related to its present value P by the formula: y ( t ) = P × 2 t/T . The formulas appear in Example 2 and Exercise 33 in § 4.1. If the base is b > 0 instead of 2 or 1/2, for example, y ( t ) = P × b t/ 10 , where t is in years for example , then the model says that (a) the initial vealue of y is P , and (b) the value of y is multipled by a factor of b every t = 10 years....
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida.
- Fall '08