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 2 years ago
The halflife 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.
 2 years ago
The halflife 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.

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wio
 2 years ago
Best ResponseYou've already chosen the best response.0So the equation is\[ q(t) = q_02^{kt} \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.0Now, the quantity is going to be halved each time so we know \(k\) is going to be negative. \[ q(t)=q_0\left(\frac{1}{2}\right)^{kt} \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.0We also know: \[ q(1600) = \frac{q_0}{2} = q\left(\frac{1}{2}\right)^{1} \]Since it is the halflife as well as\[ q(1600)=q_0\left(\frac{1}{2}\right)^{k(1600)}\]See the pattern?\[ 1=k(1600) \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.0Solving for \(k\) gives us: \[ k = \frac{1}{1600} \]
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