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Chapter 5 Preparation.

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A bird species in danger of extinction has a population that is decreasing exponentially. Five years ago the population was at 1400 and today only 1000 of the birds are alive. Once the population drops below 100, the situation will be irreversible. When will this happen?



The half life of aspirin in your bloodstream is 12 hours. How long will it take for the aspirin to decay to 70% of the original dosage?



The speed of the wind S (in miles per hour) near the center of a tornado and the distance d (in miles) the tornado travels are related by the model S=93(logd)+65. On March 18, 1925, a large tornado struck portions of Missouri, Illinois and Indiana with wind speed at the center of about 283 miles per hour. Approximate the distance traveled by this tornado.



A deposit of $10000 is made in a savings account for which the interest is compounded daily. The balance will double in 5 years. What is the annual interest rate for this account?



The half-life of thorium-229 is 7340 years. How long will it take for a sample of this substance to decay to 20% of its original amount?



Over a period of time, a hot object cools to the temperature of the surrounding air. This is described mathematically by Newton’s Law of Cooling:

Where t is the time it takes for an object to cool from Toto T, C is the surrounding air temperature and k is a positive constant that is associated with the cooling object. A cake removed from the oven has a temperature of 210oF and is left to cool in a room that has a temperature of 70oF. After 30 minutes, the temperature of the cake is 140oF. What is the temperature of the cake after 40 minutes?