# Math Help - Quadratic Equation help

1. ## Quadratic Equation help

How would I solve this?

"If a radioactive substance has a half life of 14 hours, how long would it take to reach a level of 10%"

I have no idea how to do this, although I think I may have copied it down wrong.

Any help please?

2. Originally Posted by largebabies
How would I solve this?

"If a radioactive substance has a halflife of 14 hours, how long would it take to reach a level of 10%"

I have no idea how to do this, although I think I may have copied it down wrong.

Any help please?
I am not sure it is a "quadratic" function problem.
From what I know, it should be exponential, which has a form $y = ab^t$

Half life just means the time for the intial amount decreased by a half.
So if you start with a at t = 0,
at t =14,(14 hours later), y is (1/2) of a which is 0.5a.
And at t = 28, (another 14 hours later) you get (1/2) of (0.5a) which is (0.25a),
and so forth.

So you can either find two points by the reasoning above and obtain a formula for the exponential function. After that you can solve the equation y = 10%.

Or if you note that b = (0.5)^(1/14) (the growth factor) by observation then we have y= a(0.5)^(t/14) and so on.

3. I'm still somewhat confused but i'll just skip it for now, thanks for your help