SOLUTION: A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 38 hours, 50 mg of the substance remains. How many milligrams will remain after 5

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Question 1102943: A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 38 hours, 50 mg of the substance remains. How many milligrams will remain after 54 hours? (Round your answer to two decimal places.)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
100%2Ab%5E38=50
b%5E38=%281%2F2%29
log%28%28b%5E38%29%29=log%28%281%2F2%29%29
38%2Alog%28%28b%29%29=-log%28%282%29%29
log%28%28b%29%29=-log%28%282%29%29%2F38
log%28%28b%29%29=-0.0079218
10%5E%28-0.0079218%29=b
b=0.9819
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highlight%28y=100%2A%280.9819%29%5Ex%29

Question asks, what is y when x is 54?

Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by the other tutor is valid. However, with rounding error, the answer you will get with her solution (37.29mg) will NOT be correct to 2 decimal places. If you use her method, you need to keep more decimal places in your intermediate calculations in order to get an answer that is correct to 2 decimal places.

But her method is also a LOT more work than is necessary to get the answer; there is a MUCH easier and more straightforward way.

The given information tells you immediately that the half life of the substance is 38 hours.
The given time of 54 hours is 54/38 half lives.
So the amount remaining after 54 hours, rounded to 2 decimal places, is
100%2A%281%2F2%29%5E%2854%2F38%29+=+37.34