## knbarwrgwddsg one year ago 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.

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1. wio

So the equation is$q(t) = q_02^{kt}$

2. wio

Now, the quantity is going to be halved each time so we know $$k$$ is going to be negative. $q(t)=q_0\left(\frac{1}{2}\right)^{-kt}$

3. wio

We also know: $q(1600) = \frac{q_0}{2} = q\left(\frac{1}{2}\right)^{1}$Since it is the half-life as well as$q(1600)=q_0\left(\frac{1}{2}\right)^{-k(1600)}$See the pattern?$1=-k(1600)$

4. wio

Solving for $$k$$ gives us: $k = -\frac{1}{1600}$

5. wio

@knbarwrgwddsg get it?