+484 if a sample of radioactive material of 355g and a half-life of 3.75years. The remaining sample is 22.1875g how many half-lives have the material gone through and how old is the material?
+129852 Don't know about the big brain part....but.....we have this exponential decay form :
22.1875 = 355 (1/2)^(t / 3.75) we want to find "t"
Divide both sides by 355
22.1875 / 355 = (1/2)^(t/3.75) take the log of both sides
log ( 22.1875 / 355) = log (1/2)^(t / 3.75) and we can write
log ( 22.1875 / 355) = (t / 3.75) * log (1/2) divide both sides by log (1/2)
log ( 22.1875 / 355) / log (1/2) = t / 3.75 multiply both sides by 3.75
3.75 log ( 22.1875 / 355) / log (1/2) = t = 15 years old
Note that since a half-life lasts 3.75 years....it has gone through
15 / 3.75 = 4 half-lives
That worked out kinda' nice and neat .....!!!
