Question

A researcher claims that an ancient scroll originated from greek scholars in about 500 bce. a measure of its carbon-14 decay rate gives a value that is 89% of that found in living organisms. how old is the scroll? (the half-life of carbon-14 is 5730 yr.) express the time in years as an integer.

Answer 1

The amount of substance present in a certain object with a given half-life in terms of h can be expressed through the equation,

     A(t) = (A(o))(0.5)^(t/h)

where A(t) is the amount of substance after t years and A(o) is the original amount. In this item we are given that A(t)/A(o) is equal to 0.89. Substituting the known values,

     0.89 = (0.5)(t / 5730 years)

The value of t from the equation is 963.34 years.

Answer: 963 years