A certain radioactive isotope has a half-life of approximately 900 years. How many years would be required for a given amount of this isotope to decay to 70% of that amount?

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A certain radioactive isotope has a half-life of approximately 900 years. How many years would be required for a given amount of this isotope to decay to 70% of that amount?

Mathematics
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A=A0 e^rt
1/2 = e^r(900)
solve for r

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can you continue and show work
\[e^{900r}=1/2\] 900 r ln e= ln 1/2 900 r= ln 1/2
i have an idea
write the formula as \[Q = Q_0(\frac{1}{2})^{\frac{t}{900}}\]
set \[.7=(\frac{1}{2})^{\frac{t}{900}}\] and solve for t
\[ln(.7)=\frac{t}{900}\times ln(\frac{1}{2})\]
\[t=\frac{900ln(.7)}{ln(\frac{1}{2})}\]
if you want to do it the first way using \[Q=Q_0e^{rt}\] then first you have to solve for r, then set the result equal to 1/2 and solve for t. it will work and you will get the same answer, but it is extra work
ok. i see thank you
imaram started the problem for you but you still have to solve for r, replace it in the equation, set = to 1/2 and then solve for t.

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