Question

Carbon-14 has a half life of 5730 years. A bone sample from a bird has 80% of its original Carbon-14. Fine how long ago the bird lived.

Answer 1

Answer:

1845 years

Step-by-step explanation:

Decay of Carbon-14 is usually modeled by an exponential function. It x is the number of years since the original amount was brought into existence, then the fraction remaining (y) is modeled by ...

... y = (1/2)^(x/5730)

We want to find the value of x when y = 80% = 0.80. The equation is then ...

... 0.80 = 0.50^(x/5730)

Taking logarithms, we get

... log(0.80) = (x/5730)·log(0.50)

Multiplying by the inverse of the coefficient of x, we have

... x = 5730·log(0.80)/log(0.50) ≈ 1845 . . . . years