# Pre Calc

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The half-Life 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

• Pre Calc -

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 half-life, we could use the equation

10 = 100 (.5)^(t/2651)
t/2651 = l .1 / ln .5
t = 8806

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