Exponential Growth and Decay; Modeling Data

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Presentation transcript:

Exponential Growth and Decay; Modeling Data

1. The exponential model describes the population of a country, A in millions, t years after 2006. Use this model to Find the population in 2006

2. The exponential model describes the population of a country, A in millions, t years after 2006. Use this model to when will the population be 1350 million

3. a) In 2000 the population of a country is 2 3. a) In 2000 the population of a country is 2.1 million, in 2020, the population has increased to 3.2 million, use the exponential growth model: A = A0ekt, in which t is the number of years after 2000, to find the exponential growth function that models the data b) In which year will the population be 9 million?

4. Complete the table. Round projected populations to one decimal place and values of k to four decimal places Country 2007 Population (millions) Projected 2025 Population (millions) Projected Growth Rate, k A 143.2 0.0123

5. Complete the table. Round projected populations to one decimal place and values of k to four decimal places Country 2007 Population (millions) Projected 2025 Population (millions) Projected Growth Rate, k B 19.1 30.8

6. An artifact originally had 16 grams of carbon-14 present 6. An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e-0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 10,000 years?

7. The half-life of the radioactive element plutonium-239 is 20000 years. If 20 grams of plutonium-239 are initially present, how many grams are present after 20000 years, 40000 years, 60000 years?

8. Use the exponential decay model for carbon-14, A = A0e-0. 000121t 8. Use the exponential decay model for carbon-14, A = A0e-0.000121t. Skeletons were found at a construction site in San Francisco in 1989. The skeletons contained 20% of the original carbon-14. Estimate the age of the paintings.

Radioactive Substance 9. Complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Half-Life Decay Rate, k A 5.2% per year = -0.052

Radioactive Substance 10. Complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Half-Life Decay Rate, k B 4300 years

Radioactive Substance 11. Complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Half-Life Decay Rate, k C 200 hours

12. Given interest is being compounded monthly, principle is 2,000, time is 2 years and rate is 3%, find the ending amount.

13. Given interest is being compounded quarterly, ending amount is 5,000, time is 5 years and rate is 4%, find the beginning amount (principle).

14. Given interest is being compounded daily, ending amount is 6,000, beginning amount was 5,500 and rate is 7.2%, find the time.

15. Given interest is being compounded semi-annually, ending amount is 7,000, beginning amount was 5,000 and time was 30 years, find the rate.

16. Given interest is being compounded continuously, principle is 2,000, time is 2 years and rate is 3%, find the ending amount.

17. Given interest is being compounded continuously, ending amount is 5,000, time is 5 years and rate is 4%, find the beginning amount (principle).

18. Given interest is being compounded continuously, ending amount is 6,000, beginning amount was 5,500 and rate is 7.2%, find the time.

19. Given interest is being compounded continuously, ending amount is 7,000, beginning amount was 5,000 and time was 30 years, find the rate.

20. Given interest is being compounded continuously, beginning amount was 2000 and rate is 4.1%, find out how long it will take the money to double.