# 1140 L24 - y t y t y t

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Lecture 24: Section 3.5 Exponential and Logarithmic Models Three common types of mathematical models involv- ing exponential functions and logarithmic functions: 1. Exponential growth model: y = ae bt where y = amount at time t a = amount at time 0 b = relative growth rate, b > 0 (in decimal) t = time t y NOTE: If the doubling time T is given, then b = ln 2 T

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ex. A certain breed of rabbit was introduced onto a small island 8 years ago. The current rabbit pop- ulation on the island is estimated to be 4100, with a relative growth rate of 55% per year. 1) What was the initial size of the rabbit population? 2) Estimate the population 2 years from now. 3) How long does it take the population to double?
2. Exponential decay model: y = ae ± bt where y = amount at time t a = amount at time 0 b = relative decay rate, b > 0 t = time t y NOTE: If the half life T is given, then b = ln 2 T

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A radioactive material decays according to the model y = ae ± 0 : 0244 t . Assume that a scientist has a sample of 500 grams of it. 1) What is its decay rate?
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## This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.

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1140 L24 - y t y t y t

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