posted by Laura Hieb on .
Only 27% of the carbon-14 in a wooden bowl remains. How old is the bowl? (Carbon-14 has a half-life of 5,700 years.)
Let T be the age in years.
0.27 = (0.5)^(T/5700)
Take logs of both sides to solve.
T/5700 = log(0.27)/log(0.5) = 1.889
T = ___ years
well the bowel has 27% carbon-14 remaining which means that 73% of the carbon-14 has already been depleted. 5700 years is the half life of carbon-14 so to get the full life we multiply 5700(2)=11400 years. then we can do an easy cross multiplication problem to figure it out, x/11400=73/100 and then we solve for x which is x=11400(73)/100 and the final answer and age of the bowel is 8322 years. a very algebraic way of solving it lol