Exponential Growth and Decay Objective: Determine the multiplier for exponential growth and decay.

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.

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.

Exponential Expressions

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.

Example 1

Example 1

Example 1

Example 1

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.

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.

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.

Modeling Biological Decay

Modeling Biological Decay

Example 2

Example 2

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.

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.

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