6.8Growth &amp; Decay

6.8Growth &amp; Decay - 6.8 Growth and Decay Law of...

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6.8: Growth and Decay Law of Uninhibited Growth or Decay, says that an amount A varies with time t according to the model: A (t) = A 0 e kt , where A 0 is the original amount at t = 0 and k 0 is a constant. If k > 0 , then A is increasing over time (growth); if k < 0 , then A is decreasing over time (decay). Newton’s Law of Cooling, which says that the temperature of a heated object decreases exponentially with time toward the temperature of its surroundings: u(t) = T + (u 0 – T)e kt , k < 0, where T is the constant surrounding temperature and u 0 is the initial temperature of the heated object. Logistic Growth Model, which says that growth is limited: P(t) = c ae bt 1 + - , were a, b , and c are constants with b > 0 and c > 0; c represents the carrying capacity or maximum value that the function can attain. 1. A culture of bacteria obeys the law of uninhibited growth. If 500 bacteria are present initially and there are 800 after 1 hour, how many will be present in 5 hours? How long will it take for the

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6.8Growth &amp; Decay - 6.8 Growth and Decay Law of...

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