# End Amt =Start Amt *e^-0.0391 * t (in years) Half-life =?

Gold Member
I know how to do half life problems and I even have a half-life calculator on my website:
http://www.1728.org/halflife.htm

However, I cannot calculate half-life when problems are stated in this form:
End Amt = Start Amt * e^-0.0391 * t (in years)
Half-life =?

I know calculus but I find it difficult understanding that kind of equation.

I believe the figure 0.0391 is the function "lambda".
So if lambda = .0391
then
half-life = ln(2) / lambda
half-life = 0.6931 / 0.0391
half-life = 17.73 years
Did I get that right?

## Answers and Replies

Ygggdrasil
Science Advisor
Gold Member
The half life is the value of t for which End Amt = 0.5 * Start Amt.

Gold Member
End Amt = Start Amt * e^-0.0391 * t (in years)
So the equation becoames
.5 = 1.0 * e^-0.0391 * t
Taking logs of both sides
ln (.5) = -0.0391 * t (since ln (e) = 1)
t = ln (.5) / -0.0391
t = -0.6931471806/ -0.0391
t = 17.73 years
which is what I calculated when using the "lambda" function
So I guess that is it.
Thank you. :-)

• Chestermiller and Ygggdrasil