Exponential and Decay

Question

The isotope carbon-14 has a half-life of 5,730 years. This is used to determine the age of

certain archeological discoveries.

Consider the function that represents the amount of carbon-14 in an archeological

discovery.

Part A: Define a variable for the function and state what the variable represents.

Part B: What is a reasonable domain for the situation?

Part C: If a fossil has 240 moles of carbon-14, then write the function that represents the

age of the archeological discovery.

Part D: How much carbon-14 is in the fossil in 14 half-lives (or 80,220 years)?

Answer 1

1/2 = e^5730r where r= annual decay rate, 5730 = t years for half life

take natural logs

ln.5 = 5730r

r = ln.5/5730=K= about 1.24x10^-4 = .000124 = .0124%

C(t) = (Co)(e^Kt

C(t) = (Co)(e^1.24tx10^-4

C(t) = Carbon at time t years

Co= amount of carbon when the organism dies = 1ppt

so

C(t) = e^1.24t(10^-4)