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A-CED.1

A-CED.1. I can interpret word problems and form exponential equations in order to solve a problem. Example 1. The population of a town is currently 6000 people and is expected to triple every 5 years. How many people will be living in town in 25 years?. Example 1.

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A-CED.1

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  1. A-CED.1 I can interpret word problems and form exponential equations in order to solve a problem.

  2. Example 1 • The population of a town is currently 6000 people and is expected to triple every 5 years. How many people will be living in town in 25 years?

  3. Example 1 • The population of a town is currently 6000 people and is expected to triple every 5 years. How many people will be living in town in 25 years?

  4. Example 1

  5. Example 2 • A small town finds its population is moving to the city. Every four years the population decreases by half. After 20 years the population of the town is 2000. What was the town’s initial population?

  6. Example 2 • A small town finds its population is moving to the city. Every four years the population decreases by half. After 20 years the population of the town is 2000. What was the town’s initial population?

  7. Example 2

  8. Example 3 • A scientist has discovered a new strain of bacteria. The bacteria culture initially contained 1000 and the bacteria are doubling every half hour. How many bacteria will there be in 3 hours?

  9. Example 3 • A scientist has discovered a new strain of bacteria. The bacteria culture initially contained 1000 and the bacteria are doubling every half hour. How many bacteria will there be in 3 hours?

  10. Example 3

  11. Example 4 • A radioactive isotope decays exponentially. The time it takes for half of the amount to decay is called the isotope’s half-life. A certain isotope has a half-life of 10 hours. After 40 hours there are 0.25 mg left. What was the isotope’s initial mass?

  12. Example 4 • A radioactive isotope decays exponentially. The time it takes for half of the amount to decay is called the isotope’s half-life. A certain isotope has a half-life of 10 hours. After 40 hours there are 0.25 mg left. What was the isotope’s initial mass?

  13. Example 4

  14. Example 5 • Detroit finds its population decreasing fast as people from the inter-city wish to live in the suburbs. Every six years the population decreases by 30%. After 18 years the population of the city was 337,465. What was the city’s initial population?

  15. Example 5 Detroit finds its population decreasing fast as people from the inter-city wish to live in the suburbs. Every six years the population decreases by 30%. After 18 years the population of the city was 337,465. What was the city’s initial population?

  16. Example 5 The original population of Detroit was approximately 983,863.

  17. Example 6

  18. Example 6 Katelyn purchased $2200 of Forever Fitness Footwear stock. The value of the stock is expected to increase by 8.75% per year. When will Katelyn’s stock be worth $3500?

  19. Example 6

  20. Homework 1 • A dust bunny gathers dust at a rate of 9% per week. The dust bunny originally weighs 0.75 oz. How much does the dust bunny weigh after 16 days?

  21. Homework 1 After sixteen days the dust bunny will weigh approximately 0.91 ounces.

  22. Homework 2 • In 2009, Lynn received $10,000 from her grandmother. Her parents invested all the money, and by 2021, the amount will have grown to $16,960. Write an exponential function that could be used to model the • money, y. Write the function in terms of x, the number of years since 2009. Then assuming that the amount of money continues to grow at the same rate. What would be the balance in the account in 2031?

  23. Homework 2 The value in the account in 2031 would be approximately $26,337.

  24. Homework 3 • The half-life of radium 226 is 1602 years. If you have 325 grams of radium present after 4520 years, how much radium was present originally?

  25. Homework 3 Originally there was approximately 2297 grams of radium 226 present.

  26. Homework 4 • The population of Snowtop, Colorado is currently 2300 people and it is expected to triple every 5 years. How many people will be living in the town after 20 years.

  27. Homework 4 Snowtop’s population is expected to be 186,300 after 20 years.

  28. Homework 5

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