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Algebra II Exponential Growth and Decay Name________________ Date_________________ Directions: Solve each problem. Be sure to SHOW ALL WORK!!! Circle your answer. This assignment is due Tuesday, June 5, 2016. 1. A colony of bacteria grows exponentially. The colony begins with 25 bacteria, but after 5 hours the beginning of the experiment, it has grown to 120 bacteria. a) What is the growth factor of the function used to express this problem? (Be sure to keep your answer in radical form) b) Exactly how long does it take the colony to grow to six times its original size? 2. Borat recently told me that the current population of Kazakstan is approximately 4,700,000 people and has a continuous growth rate of 2.75%. He also informed me that the neighboring country of Uzbekistan has a population of 3,850,000 people and has a continuous growth rate of 3.27% With this information, determine how many years it will take for these neighboring countries to have equal populations. 3. A bacteria colony is calculated to have 1200 cells at 12:00 in the afternoon. Three hours later, the colony has a population of 1500 cells. How many cells will there be at 9:00 at night? Algebra II Exponential Growth and Decay Page 2 4. A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one-hundred fifty bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant "b" for the bacteria? (Round b to two decimal places.) 5. A rubber ball is dropped onto a hard surface from a height of 9 feet, and it bounces up and down. At each bounce, the ball rises to 74% of its previous height. a) How high will the ball bounce after the 8th bounce? b) How many bounces will it take before the ball rises no higher than 3 inches? 6. A 15-g sample of radioactive iodine decays in such a way that the mass remaining after t days is given by m(t ) 15e .087t , where m is measured in grams. After how many days is there only 6 grams remaining? Algebra II Exponential Growth and Decay Page 3 7. The exponential growth model A 25e 0.198026t describes the population of a city in the United States, in thousands, t years after 1994. Use this model to solve the following: a What was the population of the city in 1994? b By what % is the population of the city increasing each year? c What will the population of the city be in 2005? d When will the city’s population be 60 thousand? 8. The Philadelphia Art Museum recently purchased a bronze statue of Mr. C for $400,000. After having it appraised, they learned that, on average, it will lose 10% of it’s value every year. a) Estimate the value of the statue after 6 months. b) Estimate the value of the statue after 3 months. c) Estimate how many years it will take before the statue is worth half of its purchase price. 9. The population of Mexico was 100.4 million in 2000 and is expected to grow exponentially at a rate of 1.4% per year. a) Estimate Mexico’s population in 2010. b) When will Mexico’s population reach 125 million? Algebra II Exponential Growth and Decay Page 4 10. Suppose that the population of a colony of bacteria increases exponentially. At the start of an experiment, there are 6,000 bacteria, and one hour later, the population has increased to 6,400. How long will it take for the population to reach 10,000? Round your answer to the nearest hour. 11. Suppose that at the start of an experiment there are 8,000 bacteria. A growth inhibitor and a lethal pathogen are introduced into the colony. After two hours 1,000 bacteria are dead. If the death rates are exponential, (a) how long will it take for the population to drop below 5,000? (b) How long will it take for two-thirds of the bacteria to die? Round your answers to the nearest tenth. 12. Matt bought a new car at a cost of $25,000. The car depreciates approximately 15% of its value each year. a.) What is the decay factor for the value of this car? b.) Write an equation to model the decay value of this car. c.) What will the car be worth in 10 years?