Applications of Exponential Functions -- Section 4.2 --

 Radioactive Decay  (Half-life): A = Ao2-t/h    where A = Amount, Ao is initial amount when t = 0 and h is half-life The half-life of radioactive radium Ra226 is 1,620 years. How much of a 100 gram sample will remain after 500 years?
 Solve Step Calculator Help Find A using A = Ao2-t/h Half-life formula Most calculators....use ^ or xy for exponent key Identify each part HINT: use these key strokes Ao= 100 initial amount 500 × 2 ^ (-500÷1620) [enter or =] t = 500 time in years h = 1620 half-life in years A = 500(2)-500/1620  » 403.7 Half-life Half-life means there is half the original (initial) amount left after t years. Interpret Þ There would be about 404 grams of radioactive radium left after 500 years.  The half-life of radioactive plutonium Pu226 is 24,360 years. How much of a 4,000 gram sample will remain after 30,000 years? [Solution]  The population of a country increases according to the model: P = 200e0.03t where t is time in years with t = 0 corresponding to 1995. Find the population in 2010. (population given in millions: 200 represent 200,000,000)

 Population Growth : P = Poekt    where P = population, Po is initial population when t = 0 and k is annual growth rate

 Solve Step Calculator Help Find P using P = Poekt Growth formula Most calculators....use ^ or xy for exponent key Identify each part HINT: use these key strokes Po= 200 initial amount in millions 200×e ^ (0.03×15) [enter or =] t = 15 time in years 2010 - 1995 = 15 Recall e » 2.718281828459045.... k = 0.03 growth constant - given k = 0.03 P = 200e0.03(15)  » 313.7 Growth formula You will find k in using logarithms in latter sections. Interpret Þ There would be about 313.7 million people in the year 2010.  The population of a country increases according to the model: P = 100e0.008t where t is time in years with t = 0 corresponding to 2000. Find the population in 2020.(population given in millions: 100 represent 100,000,000) [Solution]  The concentration x of a certain drug in an organ after t minutes is given by x = 0.07(1 - e-0.1t ). Find the concentration of the drug at 1 hour.

 Solve Step Calculator Help Find x using x = 0.07(1 - e-0.1t ) Given concentration formula Most calculators....use ^ or xy for exponent key Identify each part HINT: use these key strokes t = 60 Since 60 minutes = 1 hour 0.07×(1 - e ^ (-0.1×60))   [enter or =] x = 0.07(1 - e-0.1(60) ) » 0.0698 Growth formula You need both sets of parentheses. Interpret Þ There would be about 7% of the drug remaining in the organ after 1 hour.  The concentration x of a certain drug in an organ after t minutes is given by x = 0.05(1 - e-0.2t ). Find the concentration of the drug at 30 minutes. [Solution] Tutorials and Applets by
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