Question

The half-life of radium is 1600 years. If the initial amount is
q0 milligrams,
then the quantity
q(t)
remaining after t years is given by
q(t) = q02kt.
Find k.

Answer 1

something wrong here

Answer 2

so after 1600 years the amount q0 has halved. i.e. q0/2=q0*2*k*1600, rearrange and solve for k

Answer 3

maybe
\[Q(t)=Q_0\times 2^{kt}\]?

Answer 4

how can we solve it??????

Answer 5

the half life is \(1600\) years, so the model will be
\[Q=Q_0\times \left(\frac{1}{2}\right)^{\frac{t}{1600}}\]

Answer 6

oh okay thanks

Answer 7

since you are using a base of 2 instead of \(\frac{1}{2}\) you can write it as
\[Q=Q_0\times 2^{-\frac{t}{1600}}\]

Answer 8

so i guess \(k=-\frac{1}{1600}\)

Answer 9

- 1/1600