SOLUTION: At the beginning of an experiment, a scientist has 256 grams of radioactive goo. After 105 minutes, her sample has decayed to 16 grams. What is the half-life of the goo in minu

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Question 1004575: At the beginning of an experiment, a scientist has 256 grams of radioactive goo. After 105 minutes, her sample has decayed to 16 grams.
What is the half-life of the goo in minutes?

Find a formula for G(t), the amount of goo remaining at time t. G(t) =

How many grams of goo will remain after 17 minutes?

Found 2 solutions by josgarithmetic, rothauserc:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
G=256%2Ae%5E%28-kt%29 decay model

ln%28G%29=ln%28256%29-kt
ln%28G%29-ln%28256%29=-kt
highlight_green%28kt=ln%28256%29-ln%28G%29%29
k=%281%2Ft%29ln%28256%2FG%29
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k=%281%2F105%29%28ln%28256%2F16%29%29
highlight%28k=0.02641%29 based on minutes and grams

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HALF-LIFE
t=ln%28256%2F128%29%2F0.02641
highlight%28t=26.25%2Aminutes%29

Use the model as G=256%2Ae%5E%28-0.02641%2At%29 for t=17 to find how much remains after that amount of time.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Our half-life formula is
G(t) = Ao * (1/2)^(t/h), where h is the half-life and A0 is the beginning amount
16 = 256 * (1/2)^(105/h)
1/16 = (1/2)^(105/h)
use definition of logarithm
105/h = log (base 1/2) of 1/16
105/h = 4
h = 105/4 = 26.25 minutes
half-life is 26.25 minutes
********************************************************************************
we use our formula for t = 17
G(17) = 256 * (1/2)^(17/26.25)
G(17) = 163.413226968 approx 163.4
There is 163.4 grams of goo after 17 minutes