SOLUTION: At the beginning of a study, there are 50 grams of a substance present. After 17 days, there are 38.7 grams remaining. What is the rate of decay? How much of the substance will be

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Question 126381: At the beginning of a study, there are 50 grams of a substance present. After 17 days, there are 38.7 grams remaining. What is the rate of decay? How much of the substance will be present after 40 days? Assume the substance decays exponentially. Please help me.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
At the beginning of a study, there are 50 grams of a substance present. After 17 days, there are 38.7 grams remaining. What is the rate of decay? How much of the substance will be present after 40 days? Assume the substance decays exponentially.
:
Using the decay formula: A = Ao[2^(-t/h)] to find the half-life for the substance.
where:
A = resulting amt (38.7 grams)
Ao = initial amt (50 grams)
t = time (17 days)
h = half-life of the substance
:
50*(2^(-17/h)) = 38.7
:
2^(-17/h) = 38.7%2F50; divided both sides by 50
:
Find the nat log of both sides:
ln%282%5E%28-17%2Fh%29%29 = ln%2838.7%2F50%29
:
%28-17%2Fh%29%2Aln%282%29 = ln%2838.7%2F50%29; log equivalent of exponents
:
-17%2Fh*(.693147) = -.25618
:
-17 * .693147 = -.25618h; multiplied both sides by h
:
-11.7835 = -.25618h
:
h = %28-11.7835%29%2F%28-.25618%29
h = 46 days for half of it to decay
:
:
Check solution this way on a calc
enter 50*2^(-17/46)= 38.70; confirms our solution