SOLUTION: Another equation used to determine the decrease in mass, M, in milligrams, of a radioactive isotope after t years is {{{ M=100e^(-0.035t) }}}. How many years will it take a substan

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Another equation used to determine the decrease in mass, M, in milligrams, of a radioactive isotope after t years is {{{ M=100e^(-0.035t) }}}. How many years will it take a substan      Log On


   

Question 1113185: Another equation used to determine the decrease in mass, M, in milligrams, of a radioactive isotope after t years is +M=100e%5E%28-0.035t%29+. How many years will it take a substance to degrade from 100 mg to 30 mg?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Another equation used to determine the decrease in mass, M, in milligrams, of a radioactive isotope after t years is M+=+100%2Ae%5E%28%28-.035t%29%29. How many years will it take a substance to degrade from 100 mg to 30 mg?
:
100%2Ae%5E%28%28-.035t%29%29+=+30
e%5E%28%28-.035t%29%29+=+30%2F100
e%5E%28%28-.035t%29%29+=+.3
ln%28e%5E%28%28-.035t%29%29%29+=+ln%28.3%29
log equiv of exponent, find the ln, the ln of e = 1
-.035t = -1.2034
t+=+%28-1.2034%29%2F%28-.035%29
t = 34.4 years