Posted by **Jillian** on Wednesday, August 22, 2012 at 9:28am.

How do you set up this problem?

The decay constant for the radioactive element cesium 137 is .023 when time is measured in years. Find its half-life.

- Calculuc -
**drwls**, Wednesday, August 22, 2012 at 9:33am
e^(-0.023t) = 0.5

Take natural log of both sides.

-0.023 t = -0.6932

t = 30 years

- Calculuc -
**Reiny**, Wednesday, August 22, 2012 at 9:39am
If you are using the standard decay function equation

amount = initial amount e^-kt, where k = .023 then

.5 = e^ -.023t

-.023t = ln .5

t = ln .5/-.023 = 30.14 years

check: pick 500 grams

amount = 500 e^(-.023(30.14))

= 500 e^ -.69314..

= 250

YUP!!!

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