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

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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Answer 2

`k = (-1)/(1600)`

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((1)/(2))^(-kt)`

we know that

`q(1600) = (q_o)/(2) = q(1)/(2)^(1)` ....1

as it is half life so we have

`q(1600) = q(1)/(2)^(-k(1600))` ......2

comparn 1 and 2 we get

1 = - k(1600)

`k = (-1)/(1600)`