If we start with Q milligrams of radium, the amount (q) remaining after T years is given by q=Q(2)^(-T/1600). Express T in terms of q and Q?

1 Answer
May 15, 2018

T=1600/log2log(Q/q)

Explanation:

q=Qxx2^(-1/1600T)

Take logs of both sides, where log means log to any base.

logq=log(Qxx2^(-1/1600T))

Using the multiplication law

logq=logQ+log(2^(-1/1600T))

Using the powers law

logq=logQ-1/1600Tlog2

logQ-logq=1/1600Tlog2

T=1600/log2(logQ-logq)

T=1600/log2log(Q/q)