Question

@whpalmer4
half life of element is about 1200 years. after 3700 years what percentage P of a sample of this element remains? (round to nearest 10th)

Answer 1

Okay, we're halving the amount every 1200 years, so you can just write down the equation:

\[P(t) = 2^{-t/1200}\]

At \(t=0\), that gives you \(P(t) = 2^0 = 1\).
At \(t=1200\), that gives you \(P(1200) = 2^{-1200/1200} = 2^{-1} = 0.5\)
At \(t = 2400\), that gives you \(P(2400)=2^{-2400/1200} = 2^{-2} = 0.25\)

All you have to do is compute \[P(3700) = 2^{-3700/1200} =\]

Answer 2

As \(3600/1200 = 3\), this should be just a bit less than \(2^{-3} = 0.125\) Don't forget to multiply your decimal by 100% to get a percentage, and round to the appropriate place.

Answer 3

so .1179842891 rounded to tenth is just .1 then?

Answer 4

0.117984*100% = 11.7984%, round that to the nearest 10th...