SOLUTION: Find the half-life to the nearest tenth of a year of a radioactive substance that decays from 65 mg to 17.55 mg in 20years according to the exponential decay model y = ae^−bx

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Question 975956: Find the half-life to the nearest tenth of a year of a radioactive substance that decays from 65 mg to 17.55 mg in 20years according to the exponential decay model y = ae^−bx where a is the initial amount and y is the amount remaining after x years.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%2Ae%5E%28-bx%29

ln%28y%29=ln%28a%29-bx
ln%28y%29-ln%28a%29=-bx
ln%28a%2Fy%29=bx
b=%281%2Fx%29ln%28a%2Fy%29

VALUE OF b:
%281%2F20%29ln%2865%2F17.55%29
highlight%28b=0.06547%29

FIND HALF-LIFE:
ln%28a%2Fy%29=bx, from earlier step,
x=%281%2Fb%29ln%28a%2Fy%29
x=%281%2F0.06547%29ln%281%2F%281%2F2%29%29
highlight%28x=%281%2F0.06547%29ln%282%29%29
-----That will be the half-life. You can finish computing it.