SOLUTION: 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.

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Question 1130123: 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.)
My previous answers have been:
250*2 (-t/h)
250*(.5)^t
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.)
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y = a*b^t
32 = 250*b^t
32 = (250 grams)*k^(250 min)
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Cheers,
Stan H.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
f=250%2Ab%5Et

250b%5E250=32
b%5E250=32%2F250
b%5E250=16%2F125
250%2Alog%28%28b%29%29=log%28%2816%2F125%29
log%28%28b%29%29=%281%2F250%29%2Alog%28%2816%2F125%29%29
log%28%28b%29%29=-0.0035711
b=0.991811
-
half-life:
1%2A0.991811%5Ex=1%2F2
x%2Alog%28%280.991811%29%29=log%28%280.5%29%29
x=log%28%280.5%29%29%2Flog%28%280.991811%29%29
x=84.3minutes

highlight_green%28f=250%2A%281%2F2%29%5E%28t%2F84.3%29%29