A radioactive isotope has a half-life of 14 hours. Find the amount of the isotope left from a 320-milligram sample after 42 hours. If necessary, round your answer to the nearest thousandth.

Question

imstuck · Answer

You need to solve for k, the constant of decay.  The formula for that is this:$$k=\frac{ -\ln(.5) }{14 }$$(the 14 is the half life they gave you.)

imstuck · Answer

solving for k here, you get k = .0495

imstuck · Answer

Now that you have k, you can fill it into your decay formula. That is$$N=N _{0}e ^{(-k)(t)}$$where N is the amount remaining (which is what you are looking for here), N_0 is the original amount, -k is your k value with a negative in front of it (k is always negative in decay problems; it is positive in exponential growth problems), and t is the time of 42 hours (from your problem).

imstuck · Answer

Filling that in you have this:$$N=320e ^{(-.0495)(42)}$$Use you calculator to find e^(-.0495)(42).

imstuck · Answer

e^-2.079=.1251

imstuck · Answer

Multiply that by 320 and you have your answer.  It would be 40.018 mg.

imstuck · Answer

Let me know if there is any part of that you don't understand, ok?