7.6 - Laws of Growth and Decay

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7.6 - Laws of Growth and Decay Rita Korsunsky

Theorem Proof :

Example 1 The number of bacteria in a culture increases from 600 to 1800 in two hours. Assuming that the rate of increase is directly proportional to the number of bacteria present, find: a. a formula for the number of bacteria at time t Given: b. the number of bacteria at t = 4

Example 2 Radium decays exponentially and has a half-life of approximately 1600 years. a. find a formula for the amount y remaining from 50 milligrams of pure radium after t years Given: b. when will the amount remaining be 20mg?

Example 3 The maximum population of the earth is 50 Billion people. In 1980 the population was 4.5 Billion. Assuming that the population increases at a rate of 2% and the rate of increase is directly proportional to the number of people , in how many years will the maximum population be reached? Given:

Example 4 Newton’s law of cooling states that the rate at which an object cools is directly proportional to the difference in temperature between the object and the surrounding medium. If an object cools from 125° F to 100° F in half an hour with surrounding temperature at 75° F, what’s the temperature at the end of the next half hour? Let y = temperature of the object after t hours of cooling. Temperature of the surrounding medium is75°,so the difference in temperature is y - 75 Given: