Question

carbon 14 has a hlf life of 5700 years. scientists use this fact to determine the age of things made up of organic material. Suppose the average page of a book containing approximitly .5 mg og carbon 14 was put into a time capsule. How much carbon14 will each page contain after each of the following of years? a. 5700 b. 11400 c. 22800 d. 34200

Answer 1

If a(t) is the amount of C14 after t years,

a(t) = .05 * 2^(-t/5700)

do you see why this works? every 5700 years, the exponent of t decreases by 1, from 0 to -1 to -2, etc. making the multiplier 1, 1/2, 1/4, ...

a(5700) = .05*2^(-1) = .025
a(11400) = .05*2^(-2) = .0125
and so on

Answer 2

13300