Exponential Functions HW Name: ____________________________ What is the growth/decay factor in 1 – 4? Assume time is measured in units given. 1. A city grows by 28% per decade. 2. A forest shrinks 80% per century. 3. A diamond mine is depleted by 1% each year. 4. Water usage is increasing by 3% each year. For questions 5 – 8, you start with 500. How many will you have after each effect? 5. 10% increase. 6. 1% decrease 7. 42% decrease 8. 42% increase followed by a 42% decrease. 9. In 1999, the population of a country was 70 million and growing at a rate of 1.9% per year. Assuming the percentage growth rate remains constant, express the population, P, of this country as a function of t, the number of years after 1999. 10. In 2002, the cost of a train ticket from Boston to New York was $62. Assume that the price rises by 10% per year. Make a table showing the price of tickets each year until 2006. 11. The mass, Q, of a sample of Tritium (a radioactive isotope of hydrogen), decays at a rate of 5.626% per year, t. Write an equation to describe the decay of a 726 gram sample. 12. Every year a lake becomes more polluted, and 2% fewer organisms can live in it. If in 2010 there are one million organisms, write an equation relating O, the number of organisms to time t, in years since 2010. 13. Draw an example of an exponential growth function and a exponential decay function: 14. The populations, P, of six towns with time t, in years, are given by: Exponential Functions HW Name: ____________________________ i) ii) v) vi) iii) iv) a) Which towns are growing in size? _______________ Which are shrinking? ________________ b) Which town is growing fastest? ______What is the annual percent of growth rate? _________ c) Which town is shrinking the fastest? _____ What is the annual percent of decay rate? ________ d) Which town has the largest initial population? ___________What town has the smallest?_________ What could be some reasons that a town shrinks? Grows? Large initial population? Small initial population? 15. Carbon is a radioactive substance used to estimate the age of organic compounds. Over time, carbon- 14 decays into a stable form. The decay rate is 11.4% every 1000 years. Write a formula for the quantity Q of a 200 g sample of carbon -14 remaining as a function of time, t, in thousands of years? 16. On August 2, 1988, a US District Court judge imposed a fine on the city of Yonkers, New York, for dying a federal court order involving house desegregation. The fine started at $100 and was to double (ie: increase by 100%) daily until the city chose to obey the court order. a) What was the daily percent of growth of the fine? b) Find a formula for the fine as a function of t, the number of days since August 2, 1988. c) If Yonkers waited 30 days before obeying the court order, what would the fine have been? A year?
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