Microsoft word - 3.2 notes and exercises

Name ____________________________________ 3.2 Notes and Exercises
Exponential Decay Model
y = I*(1 − r)t
I = the Initial Amount
r = the rate of return (%)
and t = is a unit of time

Most major cities population is declining. Detroit is a good example of this. Detroit is
declining at an average rate of 1.53% per year. If Detroit hit its peak population in 1950 of
around 1,850,000, how many people live in Detroit today?

Half-Life Model
A = A *(1
= the Initial Amount A = the Amount at Half-life
− r)t AI
r = the rate of return (%) t = is a unit of time

Half-Life is defined as the length of time it takes the quantity to decrease to half its initial
value or quantity.
Bismuth-210 is a radioactive element that decays at a daily rate of approximately 12.94%.
If a lab has a 50-gram sample, what is its half-life?
25 = 50 * (1 − .1294)t to solve for t we must use logs. First divide both sides by 50.
.5 = (1 − .1294) Next take the log on both log .5 = log(1 −.1294) which gives you log .5 = t l = so t = 5.0020489 which is approximately 5 days. Name ____________________________________ 3.2 Notes and Exercises Complete each of the following on a separate sheet of paper. 1. Give the amount of discount and the final cost of a $150 item you purchased at a 2. Give the amount of discount and the final cost of a $75 item you purchased at a 30% 3. What is the difference in the final cost of a $275 item you purchased at a 30% Off Sale and the same item purchased at a Off Sale? 4. Analyze thoroughly the difference between taking a 10% decrease followed by a
getting a10% increase and getting a 10% increase followed by taking a 10% decrease. 5. A lab has a 30-gram sample of radon-222 which decays at a rate of 16.6% per day. a. How much radon-222 is left after 2 weeks? b. How long does it take for the radon-222 to decay to 5 grams? c. What is the half-life of radon-222 to the nearest tenth of a day? 6. A lab has a 800-milligram sample of cesdium-137 which decays at a rate of 2.28% a. Give the exponential decay model equation of cesdium-137? b. How long does it take for the radon-222 to decay to 5 grams? c. What is the half-life of cesdium-137 to the nearest tenth of a year? 7. You purchase a stock for $1000 a share. Instead of gaining in value it losses value at a. Give the exponential decay model equation of the stock. b. What is the stock worth after 6 months? c. If you are only willing to lose $250, if this lose continues in how many moths should you sell the stock to the nearest tenth of a month? 8. In a healthy adult caffeine in the bloodstream decreases at an hourly rate of a. Give the exponential decay model equation of the stock. b. What is the half-life of caffeine to the nearest tenth of an hour? c. A can of Red Bull contains 100 mg of caffeine. After you drink this how much caffeine will remain in your bloodstream after 2 hours? 9. A store starts discounting an item to get rid of it. If the store takes off 10% per day on the item how long will it take a $25 item to be given away for free? That means the cost is less than .5 of a cent.

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