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

Question 127201: 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.
Answer by stanbon(75887) (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.
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You have two points: (0,50) and (17,38.7)
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Equation form: y = ab^x
38.7 = ab^17
50 = ab^0
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From the 2nd equation: a = 50
Substitute into the 1st equation to solve for "b":
38.7 = 50b^17
b^17 = 38.7/50
b^17 = 0.7740
Take the 17th root to get:
b = 0.9850
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EQUATION:
y = 50*0.9850^x
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How much of the substance will be present after 40 days?
y = 50*0.9850^40
y = 50*0.5473
y = 27.3643 grams
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Cheers,
Stan H.
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