Exercises

1. A bacteria colony initially has mass g. After two hours, the colony has mass g. Find the mass after 5 hours. Find the time it takes for the original mass of the colony to triple.
2. A metal plate that has been heated cools from to in 20 minutes when surrounded by air at a temperature of . What will the temperature of the plate be be after one hour of cooling? When will the temperature of the plate reach ?
3. Just before midday the body of an apparent homicide victim is found in a room that is kept at a constant temperature of . At 12 noon the temperature of the body is and at 1 P.M. it is . Assume that the temperature of the body at the time of death was . What is the time of death?
4. 1. Radioactive radium has a half-life of approximately 1600 years. What percentage of a present amount remains after 100 years?
   2. If radioactive material decays continuously at a rate proportional to the amount present, find the half-life of the material if after one year, 99.57 % of an initial amount still remains.