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Worksheet: Exponential Growth/Decay - B

Answer each of the following on YOUR OWN PAPER. Show all work. 1. Bacteria grows in a petri dish at a hourly rate of 6.93%. If there are 100 bacterium initially, then how long will it take for it to (a) double (b) triple (c) reach 375 2. The population of Smallville in 1890 is 6250. If the population grows at a rate of 3.25% yearly, then in what year would the population of Smallville be 1 million people? 3. Jakielite is a radioactive substance whose half life is 115 years. (a) What is the annual rate of decay? (b) How much Jakielite will there be left from 100g of it after 400 years? (c) How long will it take for the 100g of Jakielite to decay to 1 g? 4.

Carbon-14 is used to determine the age of objects. It has a half-life of 5700 years. A vase was found in China was tested and it had only 15% of its Carbon-14 remaining. If it was found this year, then in what year was it made?

5. A rumor spreads through a school. The number of people who know the rumor is modeled by the following formula: where P is the number of people knowing the rumor and d is the number of days since the rumor began. (a) (b) (c) (d) 6.

How many people know the rumor at the beginning? How many people know the rumor after 1 week? If there are 1200 students in the school, on which day will half the school know the rumor? How many days will it take before the entire school learns the rumor?

Plutonium-210 (abbreviated P-210) is a radioactive element with a half-life of 140 days. A 10g sample was found in a container (a) How much remains after 12 weeks? (b) How long will it take to decay to 1g? (c) The container had a label on it. On the label it said 5kg of Plutonum-210 (approx 11lbs). In what year what the jar filled with P-210 if it was discovered this year? (d) If another jar contained 10g of P-210 had a label marked 1999, then how much P-210 was in the jar to start?

7. An experiment of the growth rate of fruit flies began. Each day the number of fruit flies were counted and recorded. One day, someone realized that the first page of recordings was missing. The second sheet had day 12 with 200 fruit flies and day 18 with 900 fruit flies. How many fruit flies were there originally? 8. Cars depreciate in value the moment you drive it off the lot. The rate of depreciation is 0. 5% per week. If a one-year old GMC Envoy was appraised at $41,251, then what is the cost of the Envoy when it was bought?

Name_________________________________________________ Calculus
Worksheet: Exponential Growth/Decay - B
Answer each of the following on YOUR OWN PAPE...