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Exponential Growth and Decay Objective: Determine the multiplier for exponential growth and decay. Slide 2 Slide 3 Slide 4 Application: Biology Bacteria are very small single-celled organisms that live almost everywhere on Earth. Most bacteria are not harmful to humans, and some are helpful, such as the bacteria in yogurt. Slide 5 Application: Biology Bacteria are very small single-celled organisms that live almost everywhere on Earth. Most bacteria are not harmful to humans, and some are helpful, such as the bacteria in yogurt. Bacteria reproduce, or grow in number, by dividing. The total number of bacteria at a given time is referred to as the population of bacteria. When each bacterium in a population of bacteria divides, the population doubles. Slide 6 Slide 7 Slide 8 Slide 9 Slide 10 Slide 11 Slide 12 Slide 13 Slide 14 Exponential Expressions Slide 15 Modeling Human Population Growth Human populations grow much more slowly than bacterial populations. Bacterial populations that double each hour have a growth rate of 100% per hour. The population of the United States in 1990 was growing at a rate of about 8 % per decade. Slide 16 Example 1 Slide 17 Slide 18 Slide 19 Slide 20 Try This The population of Brazil was about 162,661,000 in 1996 and was projected to grow at a rate of about 7.7% per decade. Predict the population, to the nearest hundred thousand, of Brazil for 2016 and 2020. Slide 21 Try This The population of Brazil was about 162,661,000 in 1996 and was projected to grow at a rate of about 7.7% per decade. Predict the population, to the nearest hundred thousand, of Brazil for 2016 and 2020. The starting population is 162,661,000. The multiplier is 1.077. 2016 is 2 decades, so n = 2. Slide 22 Try This The population of Brazil was about 162,661,000 in 1996 and was projected to grow at a rate of about 7.7% per decade. Predict the population, to the nearest hundred thousand, of Brazil for 2016 and 2020. The starting population is 162,661,000. The multiplier is 1.077. 2016 is 2 decades, so n = 2. 2020 is 2.4 decades, so n = 2.4. Slide 23 Modeling Biological Decay Slide 24 Slide 25 Example 2 Slide 26 Slide 27 Try This A vitamin is eliminated from the bloodstream at a rate of about 20% per hour. The vitamin reaches a peak level in the bloodstream of 300 milligrams. Predict the amount, to the nearest tenth of a milligram, of the vitamin remaining 2 hours after the peak level and 7 hours after the peak level. Slide 28 Try This A vitamin is eliminated from the bloodstream at a rate of about 20% per hour. The vitamin reaches a peak level in the bloodstream of 300 milligrams. Predict the amount, to the nearest tenth of a milligram, of the vitamin remaining 2 hours after the peak level and 7 hours after the peak level. We start with 300, and the multiplier is.80. Slide 29 Slide 30 Homework Pages 358-359 15-41 odd, 47