Question 948784
The amount C of cobalt-60 (in grams) in a storage facility at time t is given by C(t) = 25e^-.14t
where time is measured in years.
How long will it take for the original amount of 25 grams of the cobalt-60 to decay to half this amount. (This time is known as the half-life of cobalt-60.)
{{{25*e^(-.14t) = 12.5}}}
{{{e^(-.14t) = 12.5/25}}}
{{{e^(-.14t) = .5}}}  
use the nat logs
{{{ln(e^(-.14t)) = (.5)}}}
log equiv of exponents
{{{-.14t*ln(e) = ln(.5)}}}
Find the ln of .5 (the ln of e is 1)
-.14t = -.693
t = {{{(-.693)/(-.14)}}}
t = 4.95 yrs
:
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Check this on your calc: enter 25*e^(-.14*4.95)