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.k =

Answer 1

Answer:

$k = \frac{-1}{1600}$

Step-by-step explanation:

Given data:

half life of radium is 1600 year

the equation is given as $q(t) = q_o 2^{kt}$

As it is given, quantity is going halved, thus k is is going to be -ve. thus equation become

$q(t) = q_o(\frac{1}{2})^{-kt}$

we know that

$q(1600) = \frac{q_o}{2} = q\frac{1}{2}^{1}$     ....1

as it is half life so we have

$q(1600) = q\frac{1}{2}^{-k(1600)}$      ......2

comparn 1 and 2 we get

1  = - k(1600)

$k = \frac{-1}{1600}$

Answer 2

P(1600)/(P0)=.5
.5=e^-1600k
ln 0.5=ln e^-1600k=-1600k ln e =-1600k
k=ln 0.5/-1600
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