30 Exponential Decay Practice
Name: _________________________
1. During normal breathing, about 12% of the air in the lungs is replaced after one breath. Write an
exponential decay model for the amount of the original air left in the lungs if the initial amount of air
in the lungs is 500 mL. How much of the original air is present after 240 breaths?
2. An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system
decreases by about 29%. How much ibuprofen is left after 6 hours?
3. You buy a new computer for $2100. The computer depreciates by 50% annually. When will the
computer have a value of $600?
4. You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases
by about 12%. How much caffeine will be in your system after 3 hours? How long until you have
10mg of caffeine?
5. Each year the local country club sponsors a tennis tournament. Play starts with 128 participants.
During each round, half of the players are eliminated. How many players remain after 5 rounds?
6. A 500 mL puddle of water is evaporating at a rate of 4% per hour. Write a function that represents
the amount of water in the puddle at a given time. Use x for hours and y for the amount of water left
in the puddle.
7. Using the equation from the above problem, determine when the puddle will be reduced to half its
original volume.
8. The population of a city can be modeled by P=10,528(0.92)t where t is the number of years since
1990. What was the population in 1990? By what percent did the population increase by each year?
9. The half life of Cs-137 is 30.2 years. If the initial mass of the sample is 1.00kg, how much will
remain after 151 years?
10. Bismuth-214 has a half-life of approximately 20 minutes. Find the amount of bismuth-214 left
from a 30-gram sample after 1 hour.
11. Mendelevium-258 has a half-life of approximately 52 days. Find the amount of mendelevium258 left from a 44 gram sample after 156 days.
12. The half-life of bromine-82 is approximately 36 hours. Find the amount of bromine-82 left from
an 80-gram sample after 6 days.