Section 3.1: 3, 4

Section 3.2: 1, 2

Also:

1. A bone fossil is determined to have 5% of its original carbon-14 remaining. How old is the fossil?
2. Plutonium-239, the fuel for nuclear reactors, has a half-life of 24,000 years. How many years will it take before there is only 10% left? How many years until only 5% remains?
3. If 1% of a certain radioactive element decays in one year, what is the half-life of the element?
4. A glass of lemonade, initially at a temperature of 40 degrees F, is placed on a table in a room held at a constant temperature of 75 degrees F. If after 10 minutes the lemonade has warmed to 48 degrees F, what is the temperature of the lemonade after 30 minutes? How long will it take the lemonade to warm to 65 degrees F?
5. A cup of coffee, initially at a temperature of 110 degrees F, is placed on a table in a room. After five minutes the coffee has cooled to 100 degrees F and after ten minutes the coffee has cooled to 92 degrees F. What is the temperature of the room?

Answers:

1. 24,064 years
2. 79,726 years; 103,726 years
3. 68.97 years
4. 58.9 degrees F; 48 minutes
5. 48.3 minutes
6. 60 degrees F