part 1 A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 40 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.)
part 2. To the nearest minute, what is the half-life of this substance?
f(t) = 250*(1/2)^(t/k)
since
f(250) = 40, we find the half-life k using
250*(1/2)^(250/k) = 40
k = 94.559
makes sense, since 40/250 is between 2 and 3 half-lives
f(t) = 250*(1/2)^(t/94.559)