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**Unformatted text preview: **Lecture 24: Section 3.5 Exponential and Logarithmic Models Four common types of mathematical models involv- ing exponential functions and logarithmic functions: 1. Exponential growth model: u1D466 = u1D44Eu1D452 u1D44Fu1D461 where u1D466 = amount at time u1D461 u1D44E = amount at time 0 u1D44F = relative growth rate, u1D44F > u1D461 = time t y NOTE: If the doubling time u1D447 is given, then u1D44F = ln 2 u1D447 ex. The population of a small town grows exponen- tially. In 1900, the population was 900. In 1920, the population had grown to 1,600. 1) What is the growth rate of the population of this town? 2) What was the population of this town in 1960? ex. A culture starts with 10,000 bacteria, and the number doubles every 40 minutes. 1) Find a function that models the number of bacteria at time u1D461 . 2) Find the number of bacteria after two hours. 3) After how many minutes will there be 50,000 bacteria? 2. Exponential decay model: u1D466 = u1D44Eu1D452 u1D44Fu1D461 where u1D466 = amount at time...

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