SOLUTION: The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. The half-life of a substance is 3.1

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Question 1058423: The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. The half-life of a substance is 3.1 years. How long will it take for 50 grams to decay to 8 grams? (Round your answer to one decimal place.)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=50%2Ae%5E%28-kt%29

ln%28y%29=ln%2850%29-kt
-kt=ln%28y%29-ln%2850%29
kt=ln%2850%29-ln%28y%29
k=%281%2Ft%29ln%2850%2Fy%29
Use halflife:
k=%281%2F3.1%29%28ln%2850%2F25%29%29
k=ln%282%29%2F3.1
highlight%28k=0.22359%29

kt=ln%2850%29-ln%28y%29
t=%281%2Fk%29%28ln%2850%2Fy%29%29
How long to reach 8 grams?
t=%281%2F0.22359%29ln%2850%2F8%29
highlight%28t=ln%2825%2F4%29%2F0.22359%29