# math

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only 5% of the carbon-14 in a small wooden bowl remains , how old is the bowl?
Hint, half-life for carbon –14 us 5730 years

• math -

Since this is a "half-life" situation we can use
1/2 or .5 as the base in our exponential equation

5 = 100 (1/2)^(t/5730)
.05 = .5 ^(t/5730)
take ln of both sides

ln 0.05 = (t/5730) ln 0.5
t/5730 = ln 0.05/ln 0.5 = 4.3219...
t = appr 24765 years

• math -

Unless your teacher gives you 5700 as the half life.

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