"the charcoal from a tree killed in the volcanic eruption that formed cedar lake in oregon contained 44.5% of the carbon-14 found in living matter. about how old is cedar lake? "

The half life of carbon-14 is 5700 years. (Half life is the time taken by a radioactive isotope to decay by half of its original mass). 
Let A₀ be the initial amount of carbon-14 that is found in living matter (t=0 years), to determine when there was 44.5% of A₀ left.
44.5 = 100 × (1/2)^n, where n is the number of half lives
0.5^n = 0.445
    n = log 0.445/log 0.5
    n = 1.168
But 1 half life is 5700 years
Therefore, the number of years will be 5700 × 1.168 = 6658.299725 years
≈ 6658.30 years

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