Exponential Decay Question!?
I don't know how to solve this.
Strontium-90 has a half-life of 25 years. How long would it take 4 mg of it to decay to 0.5 mg?
If someone could show me the steps that would be great!
I have this so far:
But I don't know how to solve for t.
Thank you for those answers, but is it possible to solve without the use of logarithms?
- Anonymous1 decade agoFavorite Answer
y = abⁿ
This formula is called Exponential Decay formula if 0 < b < 1
You substitute the variables correctly. Divide both sides by 4 first.
1/8 = (1/2)^(t/25)
Rewrite this with logs.
log(1/8) = tlog(1/2)/25
Solve for t.
log(1/8)/[log(1/2)/25] = t
t = 75
- 1 decade ago
first divide both sides by 4 to get rid of that 4 there. So you'll have:
now, take the log base (1/2) of both sides. from logarithm properties, this will cancel the (1/2) and remove the exponent, leaving the (t/25).
To do this on a calculator for the left side of the equation, divide the log(.125) by log(1/2). The answer for this is 3. Now we have:
So your answer is 75 years. Hope I helped!