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ss_4_7 - Section 4.7. Growth and Decay Exponential growth:...

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Section 4.7. Growth and Decay Exponential growth: A = A 0 e kt , k> 0 Exponential decay: A = A 0 e kt , k< 0 Note. In the above, A 0 is amount, A ,at t =0. Exponential growth and decay are shown graphically in the following diagrams. –2 –1 0 1 2 –2 –1 1 2 –2 –1 0 1 2 –2 –1 1 2 The following examples illustrate typical applications of the exponential growth and decay formulas. Example. The number, N , of bacteria in a culture is given by N = 1000 e . 001 t ,where t is time in hours. When will the population reach 2000? Solution. N = 1000 e . 001 t 2000 = 1000 e . 001 t e . 001 t =2 ln e . 001 t =ln2 . 001 t =ln2 t = ln 2 . 001 0 . 693 . 001 t = 693 hours Example. Iodine, I 131 , decays according to A = A 0 e - . 087 t ,where t is time in days. What is the half-life of I 131 ? Solution. A = A 0 e - . 087 t 1 2 A 0 = A 0 e - . 087 t 1 2 = e - . 087 t ln 1 2 =ln e - . 087 t = - . 087 t t = ln 1 2 - . 087 = ln 1 - ln 2 - . 087 . 693 . 087 7 . 97 days. Example.
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This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

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ss_4_7 - Section 4.7. Growth and Decay Exponential growth:...

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