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Chapter 6

Chapter 6. Exponential and Logarithmic Functions. Section 6.1. Exponential Growth and Decay. Modeling Bacterial Growth. You can use a calculator to model the growth of 25 bacteria, assuming that the entire population doubles every hour. Copy and complete the table below:.

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Chapter 6

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  1. Chapter 6 Exponential and Logarithmic Functions

  2. Section 6.1 Exponential Growth and Decay

  3. Modeling Bacterial Growth You can use a calculator to model the growth of 25 bacteria, assuming that the entire population doubles every hour. Copy and complete the table below:

  4. Modeling Bacterial Growth You can represent the growth of an initial population of 100 bacteria that doubles every hour by completing the table below: The population after n hours can be represented by the following exponential expression: n times

  5. Vocabulary • The expression, 100  2n, is called an exponential expression because the exponent, n, is a variable and the base, 2, is a fixed number. • The base of an exponential expression is commonly referred to as the multiplier.

  6. 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 U.S. in 1990 was growing at a rate of about 8% per decade.

  7. Modeling Human Population Growth The population of the U.S. was 248,718,301 in 1990 and was projected to grow at a rate of about 8% per decade. Predict the population, to the nearest hundred thousand, for the years 2010 and 2025. • To obtain the multiplier for exponential growth, addthe growth rate to 100%. • Write the expression for the population n decades after 1990. • How many years past 1990 is 2010? How many decades is this? • How many years past 1990 is 2010? How many decades is this?

  8. Deeper Thinking… • Why would we ADD to 100% for an exponential growth? • What does growth mean? • Don’t forget to always change your percentages to decimals and then use this as the multiplier. • What would it mean for a population to have a growth rate of 100%? • Ex: Population = 300  100% growth = ? • What would a 200% growth rate look like for this population? • Would 100% change the population? • Why do we ADD the growth rate to 100%?

  9. Modeling Biological Decay • Caffeine is eliminated from the bloodstream of a child at a rate of about 25% per hour. • A rate of decay can be though of as a negative growth rate.

  10. Modeling Biological Decay The rate at which caffeine is eliminated from the bloodstream of an adult is about 15% per hour. An adult drinks caffeinated soda, and the caffeine in his or her bloodstream reaches a peak level of 30 milligrams. Predict the amount, to the nearest tenth of a milligram, of caffeine remaining 1 hour after the peak level and 4 hours after the peak level. • To obtain the multiplier for exponential decay, subtractthe growth rate to 100%. • Write the expression for the caffeine level x hours after the peak level. • Find the remaining caffeine amount after 1 hour. • Find the remaining caffeine amount after 4 hours.

  11. Deeper Thinking… • Why would we SUBTRACT from 100% for an exponential decay? • What does the word decay mean? • Don’t forget to always change your percentages to decimals and then use this as the multiplier. • What would it mean for a population to have a decay rate of 100%? • Ex: Population = 300  100% decay = ? • What would a 25% decay rate look like for this population? • Why do we SUBTRACT the decay rate from 100%?

  12. Practice Find the multiplier ofr each rate of exponential growth or decay. • 7% growth • 2% decay • 0.05% decay • 9% growth • 8.2% decay • 0.075% growth Given x = 5, y = 3/5, and z = 3.3, evaluate each expression. • 2x • 50(2)3x • 3y • 25(2)z • 10(2)z+2

  13. Practice Predict the population of bacteria for each situation and time period (be sure to use the formula and show all work!!). • 55 bacteria that double every hour • after 3 hours • after 5 hours • 75 E.coli bacteria that double every 30 minutes • after 2 hours • after 3 hours

  14. Homework Finish worksheet 6.1 

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