SOLUTION: The radioactive substance uranium-240 has a half-life of 14 hours. The amount A(t) of a sample of uranium-240 remaining (in grams) after t hours is given by the following exponenti

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Question 852441: The radioactive substance uranium-240 has a half-life of 14 hours. The amount A(t) of a sample of uranium-240 remaining (in grams) after t hours is given by the following exponential function:

A%28t%29=2800%281%2F2%29%5E%28t%2F14%29
A(t)=2800(1/2)^t/14 (just in case the formula plotting system doesn't work.

Find the initial amount in the sample and the amount remaining after hours.
Round your answers to the nearest gram as necessary.
Initial Amount:
Amount after 40 hours:
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The radioactive substance uranium-240 has a half-life of 14 hours. The amount A(t) of a sample of uranium-240 remaining (in grams) after t hours is given by the following exponential function:

A%28t%29=2800%281%2F2%29%5E%28t%2F14%29
---------
Initial amt is A(0) = 2800 gm
----
A%2840%29+=+2800%281%2F2%29%5E%2840%2F14%29
= 386 gm
-----------
Just calculator work.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Initial amount:
A%280%29=2800%2A%281%2F2%29%5E0=2800%2A1=2800

After 40 hours:
A%2840%29=2800%2A%281%2F2%29%5E%2840%2F14%29
My calculator says 0.5^(40/14) is 0.138, and
A%2840%29=386
(I believe it because 40/14 is about 3, and (1/2)^3=1/8=0.125).