SITUATIONAL PROBLEMSINVOLVING EXPONENTIALGROWTH AND DECAY

1. Solve each problem. (6 points each) 1. The half-life of a radioactive substance is defined to be the amount of time it takes for the substance to decay 50% of its amount. If substance X has a half-life of 3,600 years, what part of substance X will remain after 4,500 years? 2. In a community with 300 families, it was found out that 50 families that were infected by the disease. After one week, the number of families that were infected by the disease was increased by 10. Assuming that the spread of disease follows a bounded growth model, when will 90% of the community be infected? 3. A thermometer reads 18C inside an air-conditioned house. It is placed outside the house where the air temperature is 30C. Three minutes later, it is found that the thermometer reading is 21C. Find the thermometer reading after 6 minutes. II. Analyze and solve the problem. (7 points) 1. Scientist stock a very large aquarium with 500 shrimps for an experiment and the aquarium can accommodate up to 10,000 shrimps tripled during the first quarter of the year. a. Assuming that the size of the shrimp population satisfies the logistic equation, find an expression for the size of the population after t quarters. b. How long will it take the population to reach 3,000