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Have you ever wondered how many people might inhabit the US in 20 years?

Have you ever wondered how many people might inhabit the US in 20 years?. For example, if the US population grows by 1.5% each year, how many people will there be in 20 years?. In this lesson you will learn how to create and graph exponential relationships by using exponential functions.

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Have you ever wondered how many people might inhabit the US in 20 years?

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  1. Have you ever wondered how many people might inhabit the US in 20 years? For example, if the US population grows by 1.5% each year, how many people will there be in 20 years?

  2. In this lesson you will learn how to create and graph exponential relationships by using exponential functions

  3. Example: You start with 25 dots, and the number of dots increase by 40% in every step. 40% growth 40% growth

  4. y = a(1+r)x y = 25(1+.4)x 40% growth 40% growth y = 25(1.4)x

  5. Exponential growth Exponential decay

  6. If the values are growing, the growth factor is greater than 1 y = 25(1.4)x If it is decaying, the decay factor is less than 1 but more than 0 y = 25(.4)x

  7. We will investigate the following: The population of the United States has grown by approximately 1.5% each year for the past 100 years. If the population of the US was 92.2 million 100 years ago, create and graph the function relating time and the population of the US.

  8. p = a(1+r)t p = (92.2)*(1+r)t 92.2 (million) start pop. p = (92.2)*(1+.015)t 1.5% growth every year p = (92.2)*1.015t

  9. p = (92.2)*1.015t population (millions) 450 400 350 300 250 200 150 100 50 0 0 50 100 time (years)

  10. In this lesson you have learned how to create and graph exponential relationships by using exponential functions

  11. We will investigate the following: During the 19th century, American settlers hunted bison almost to extinction. If 15% of the population was killed each year, and they started with an initial population of 1,000,000, create and graph the relationship between time and number of bison remaining.

  12. p = a(1+r)t p = (1000)*(1+r)t 1000 (thousands) start pop. p = (1000)*(1-.15)t 15% decay every year p = (1000)*0.85t

  13. p = (1000)*0.85t population (thousands) 1200 1000 800 600 400 200 0 0 20 40 60 time (years)

  14. Explore what effect changing the growth/decay factor has on a populations growth/decay. • Your bank account may have a “compounded interest”. Investigate compound interest and relate it to exponential functions. • Investigate the population of the world over the past 4000 years. Can the population be modeled with an exponential function. Justify your answer.

  15. 1. A population of bacteria will grow by about 20% each hour. If a colony of bacteria start with 2000, create and graph the relationship between time and colony size. 2. A certain new car’s value is said to “depreciate” (lose value exponentially) at a rate of 12% each year. If the car was originally priced at $28,000, create and graph the relationship between time and the car’s value.

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