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Half-life problem, calculus problem?
The half-life of nicotine in the blood is 2 hours. A person absorbs 0.4 mg of nicotine by smoking a cigarette. Estimate the length of time until the amount of nicotine is reduced to 0.04 mg.
I set up the problem like this but dont know how to find the answer?
0.04 = 0.4 (1/2)^t
4 Answers
- 10 years agoFavorite Answer
This isn't calculus. I don't know why people state that their problems are calculus problems when they really aren't. This is an algebra 2 problem, at best. On the plus side, you set up your equation mostly correctly
A = P * (1/2)^(t/k)
A = final amount
P = initial amount
t = elapsed time
k = half-life time
0.04 = 0.4 * (1/2)^(t/2)
0.04 / 0.4 = (1/2)^(t/2)
1/10 = (1/2)^(t/2)
log(1/10) = (t/2) * log(1/2)
-1 = (-t/2) * log(2)
2 / log(2) = t
t = 6.6438561897747246957406388589788
It takes about 6.64 hours
- 10 years ago
From your equation, we have:
10 = (1/2)^t
t = log (10)[base 1/2] ------ or ln(10) / ln(1/2)
Take note that the t you get is the number of half-lives - you will need to multiply this by 2 hours to get the amount of time.
- Anonymous7 years ago
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- KeithLv 710 years ago
0.04 = 0.4 * (1/2)^t
ln(0.04) = ln(0.4) + ln(1/2) * t
t = ( ln(0.04) - ln(0.4) ) / ln(0.5) ~ 3.3219 <=== number of half lives.
3.3219 * 2 hours = 6.6438 hours
**********
One could also use this equation and solve
0.5 = e^( - 2r) <== where 2r = 2 hours times rate per hour
r ~ 0.346574
0.04 = 0.4 e^(- 0.346574 t) <== where t = hours
t ~ 6.6438
