Half-life Equation

[katie20]

Here is the problem:

if the quantity of a substance decrease by 4% in 10 hours, find the half-life.

 

[katie20]

I have used the equation Q= Q_0(1+r)^t. I know that I need to use Q(t)=Q_0/2 after I solve the first equation. I just do not know where to start.

 

[mmm4444bot]

You could substitute three known values into your model, and solve for r.

If we let Q_0 = 100, then a 4% reduction yields Q = 96.

In other words, solve:

96 = 100(1 + r)^10

Once you know the value of r, you can solve the following for t, to get the half-life.

50 = 100(1 + r)^t

For exponential decay, I'm used to this model:

Q = Q_0 * e^(kt)

 

[lookagain]

if the quantity of a substance decrease by 4% in 10 hours, find the half-life.

katie20,

once you find the k value, you can use \(\displaystyle half\small{-}life \ = \ \frac{ln(.5)}{k}.\)