Use the decay eqtn for polonium-218, at A(t)=A_o(0.5)^(t/3.1), where A is the amount remaining after t min. and A_o is the initial amount.
a) How much will remain after 90 sec from an initial sample of 50 mg?
b) How long will it take for this sample to decay to 10% of its initial amount of 50 mg?
c) Would your answer in part b change if the size of the initial sample where changed? Explain why or why not.
My answer for part a was 35.75 mg, which is correct.
But I do not understand how to do part b and c. For part b, what I did was sub in 35.75 for A(t) and subbed in 5 (10% of 50, which is 5) for the initial amount A_o. Then, I proceeded on to solve for t.
I ended up with -9.04, but the answer is supposed to be approx 10.3 min. Could someone explain to me what I did wrong and how I can fix this?
Also, for part c, the answer in the back says "no" but I think that (even though I don't have part b done), from the answer that they give, the answer would in fact be "yes" because from part a we used 50 mg as the initial sample and that is how we calculated part b. So they must be the same, otherwise the answer would change in part b. Am I wrong on this too? Please explain why.
Thank you very much to whoever helps!