Question 1129640
A scientist begins with 250 grams of a radioactive substance.
 After 250 minutes, the sample has decayed to 32 grams. 
Write an exponential equation f(t) representing this situation. (Let f be the amount of radioactive substance in grams and t be the time in minutes.) 
To the nearest minute, what is the half-life of this substance?
: 
A = Ao*2^(-t/h) is the radioactive decay formula, where
A = remaining amt after t time (32 gr)
Ao = initial amt (250 gr)
t = time (250 minutes)
h = half-life of substance
:
250*2^(-250/h) = 32
divide both sides by 250
2^(-250/h) = .128
ln(2^(250/h)) = ln(.128)
log equiv of exponent
{{{-250/t}}}*ln(2) = ln(.128)
{{{-250/t}}} = {{{ln(.128)/ln(2)}}}
using your calc
{{{-250/t}}} = -2.9658
-2.9658t = -250
t = {{{(-250)/(-2.9658)}}}
t = 84.3 ~ 84 minutes is the half life of the substance