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]

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Joe McDonald
Community College of Southern Nevada