The halflife of plutonium241 is approximately 13 years How m

The half-life of plutonium-241 is approximately 13 years. How much of a sample weighing 8 g will remain after 100 years? How much time is necessary for a sample weighing 8 g to decay to 0.1 g? After 100 years, g will remain. Do not round until the final answer. Then round to four decimal places as needed.)

Solution

y = A* e^(.05.3t)

y= 8 * 2.71828182846^(.053(100))

y= 8 * 2.71828182846 ^-(.053(100) )

y = 8 * 2.718281828 ^-(5.3)

y= 8* 0.0049915939069102162122867259420746

y= 0.039932751 grams

proof

y= Ae^(-.053t)

y/ e^(-.053t) = A


0.039932751 / e^(-.053*100) = A

0.039932751/2.7182818284591^ (-5.3) = A

0.039932751 / 0.004991593907 = A

7.9999999998 or 8 =A

It checks and equals


Number 2 :

y= Ae^(-.053t)

y/A= e^(-.053t)

ln(y/A) = ln(e^(-.053t)

ln(y/A) = -.053t

1/-.053* ln(y/A) = -.053t* 1/-.053

ln(y/A)/-.053 = t

ln(.1/8)/-.053 = t

ln( .0125) / -.053 = t

-4.382026635/ -.053 = t

82.67974782 = t

82.67974782 years