Pre Calc
posted by Alex .
The halfLife of radioactive earthium is 2651 years. Find how many years it will take 100 grams of earthium to decay to 10 grams.
I know the equation is A=Ae^(rt)
I tried working it out but I think I am doing it wrong.
I did 10=100e^(r*2651)
Can anyone help? Thanks a lot

If you want to use the e^kt function then you can find k the following way.
.5 = 1(e^2651k)
ln .5 = 2651k
k = ln.5/2651 = .000261466
so we need:
10 = 100(e^ .000261466t)
.1 = e^ .000261466t
.000261466t = ln .1
t = ln .1 / .000261466
t = 8806 years
or
Since you know you are dealing with halflife, we could use the equation
10 = 100 (.5)^(t/2651)
t/2651 = l .1 / ln .5
t = 8806