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Section 4.6 Modeling with Exp. & Log Equations

Chapter 4 – Exponential and Logarithmic Functions. Section 4.6 Modeling with Exp. & Log Equations. Exponential Growth Doubling Time. If the initial size of a population is n 0 and the doubling time is a , then the size of the population at time t is

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Section 4.6 Modeling with Exp. & Log Equations

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  1. Chapter 4 – Exponential and Logarithmic Functions Section 4.6 Modeling with Exp. & Log Equations 4.6 - Modeling with Exp. & Log Equations

  2. Exponential Growth Doubling Time • If the initial size of a population is n0 and the doubling time is a, then the size of the population at time t is where a and t are measured in the same time units (minutes, hours, days, etc.) 4.6 - Modeling with Exp. & Log Equations

  3. Example – pg. 350 4.6 - Modeling with Exp. & Log Equations

  4. Exponential Growth Relative Growth Rate • A population that experiences exponential growth increases according to the model where n(t) = population at time t n0 = initial size of the population r = relative rate of growth (expressed as a proportion of the population) t = time 4.6 - Modeling with Exp. & Log Equations

  5. Example – pg. 350 4.6 - Modeling with Exp. & Log Equations

  6. Newton’s Law of Cooling • If D0 is the initial temperature difference between an object and its surroundings, and if its surroundings have a temperature TS, then the temperature of the object at time t is modeled by the function where k is a positive constant that depends on the type of object. 4.6 - Modeling with Exp. & Log Equations

  7. Example – pg. 352 4.6 - Modeling with Exp. & Log Equations

  8. Radioactive Decay Model • If m0 is the initial mass of a radioactive substance with half-life h, then the mass remaining at time t is modeled by the function where 4.6 - Modeling with Exp. & Log Equations

  9. Example – pg. 352 4.6 - Modeling with Exp. & Log Equations

  10. IMPORTANT!! • Make sure you READ through the other examples in Section 4.6 in the BOOK. 4.6 - Modeling with Exp. & Log Equations

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