Math Worksheet Exponential Growth and Decay

Honors Pre-Calculus Exponential Growth and Decay 3.5 D2 Worksheet Exponential Growth: Name__________________________________ Exponential Decay: ( ) ( *population growth ( Compound Interest: *population decay ) Compound Interest Continuously: ( ) Half-Life: 1. Find an exponential function having the given values. a. ( ) ( ) c. ( ) , e. ( ) , g. ( ) , , b. ( ) ( ) d. ( ) , ( ) ( ) f. ( ) , ( ) h. ( ) , ( ) ( ) ) ( ) , * is the interval of the half-life 2. Suppose the population of a nation grows at per year. If the population was , what will be the population, to the nearest million, in the year ? 3. A colony of bacteria decays so that the population days from now is given by 4. 5. a. What is the amount present when b. How much will be present in c. What is the half-life? days? b. days? c. days d. days? The half-life of radium is about after: a. b. c. d. years? years? years years? ( ) ( ) . ? days? The half-life of a radioactive isotope is after: a. people in days. If kg are present now, how much will be present years. If kg is present now, how much will be present 6. The table shows the amount ( ) in grams of a radioactive element present after days. Suppose that ( ) decays exponentially. days ( ) a. What is the half-life of the element? b. About how much will be present after c. Find an equation for ( ). days? 7. When a certain medicine enters the bloodstream, it gradually dilutes, decreasing exponentially with a half-life of days. The initial amount of the medicine in the bloodstream is milliliters. What will the amount be days later? 8. An amount of a radioactive iodine has a half-life of after days? 9. A bacteria colony triples every days later? 10. In a research experiment, a population of fruit flies is increasing according to the law of exponential growth. After days there are flies, and after days there are flies. How many flies will be there after days? days. The population is Round down to the nearest whole number. days. In terms of , how much is present bacteria. What will the population ( ) be 11. In a research experiment, a population of fruit flies is increasing according to the law of exponential growth. After days there are flies, and after days there are flies. How many flies will be there after days? Round down to the nearest whole number. 12. 13. 14. The population (in thousands) of Reno, Nevada can be modeled by corresponding to the year . In , the population was a. Find the value of b. Use your model to predict the population in where is the year, with . for the model. Round your result to four decimal places. . The population (in thousands) of Las Vegas, Nevada can be modeled by with corresponding to the year . In , the population was a. Find the value of b. Use your model to predict the population in where is the year, . for the model. Round your result to four decimal places. The initial bacterium count in a culture is and finds that the relative rate of growth is . . A biologist later makes a sample count of bacteria in the culture per hour. a. Find a function that models the number of bacteria after hours. Use b. What is the estimated count after hours? . 15. A certain breed of rabbit was introduced onto a small island about years ago. The current rabbit population on the island is estimated to be , with a relative growth rate of per year. a. What was the initial size of the rabbit population? Use b. Estimate the population years from now. 16. The population of the world in was billion, and the estimated relative growth rate was If the population continues to grow at this rate, when will it reach billion? Use 17. A culture starts with 18. bacteria and the number doubles every a. In the half-life formula, use a time . b. Find the number of bacteria after c. After how many minutes will there be A culture starts with instead of per year. minutes. to find a function that models the number of bacteria at hour. bacteria? bacteria and the number doubles every a. In the half-life formula, use a time . instead of b. Find the number of bacteria after c. After how many minutes will there be minutes. to find a function that models the number of bacteria at hours. bacteria? 19. 20. 21. A culture starts with bacteria. After hour, the count is . a. Find a function that models the number of bacteria after hours. Use b. Find the number of bacteria after c. After how many minutes will the number of bacteria double? The count in a culture was after hours. hours and after hours. a. What is the relative rate of growth of the bacteria population. Express your answer as a percentage. Use to find and . b. What is the initial size of the culture? c. Find a function that models the number of bacteria after hours. d. Find the number of bacteria after e. When will the number of bacteria be Polonium- has a half-life of hours. ? days. Suppose a sample of this substance has a mass of a. Find a function that models the amount of the sample remaining at time . b. Find the mass remaining after c. How long will it take for the sample to decay to a mass of year. mg? mg. 1a. ( ) 1b. ( ) 1c. 1e. ( ) 1f. ( ) 1g. 2. 4a. 5a. 6a. 3a. kg 6b. 8. 9. 12a. 12b. 14a. 14b. 16. years from 17b. 18c. 17c. hours 20a. 20e. kg 4c. 5b. days hours √ √ ( kg kg ( ) kg people 10. 5c. kg ( ) flies ( √ ( ) ( ) 7. or 13b. 15a. 15b. ) days 5d. 13a. flies people or ( ) 17a. ( ) 18a. 19b. 20b. 20c. ( 21b. mg ( ) 1h. 11. , or in the year minutes ( ) 4d. 6c. ( ) 1d. 3c. 19a. 21a. ) 3b. 4b. kg ( ) 18b. 19c. ) minutes 20d. 21c. days