## 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.

Source: http://hsemathtchr.info/wp-content/uploads/2013/10/32-notes-and-exercises.pdf

Fluid Phase Equilibria 207 (2003) 183–192Solubility of solid solutes in supercritical carbon dioxideQunsheng Li, Zeting Zhang, Chongli Zhong, Yancheng Liu, Qingrong Zhou Department of Chemical Engineering, Beijing University of Chemical Technology, P.O. Box 100, Beijing 100029, China Received 4 October 2002; accepted 14 January 2003 Abstract The solubility of 2-naphthol and anthracene in

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