# 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

Algebra ->  -> 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       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Mathway solves algebra homework problems with step-by-step help!

 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(16527)   (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) = ; divided both sides by 50 : Find the nat log of both sides: = : = ; log equivalent of exponents : *(.693147) = -.25618 : -17 * .693147 = -.25618h; multiplied both sides by h : -11.7835 = -.25618h : h = 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