exponential decay

Question

A mummy was recently discovered. It now contains 89.7​% of its original Carbon 14.About how old is the mummy. Assume that the​ half-life of Carbon 14 is 5730 years.ROUND YOUR ANSWER TO THE NEAREST

YEAR.The mummy is about __

years old.

Answer 1

First, set up the equation for exponential decay: f(t) = P₀e^-rt, where P₀ is the original amount of Carbon 14. To find the half life, we set the equation to half the original and t=5730.

P₀ / 2 = P₀e^-5730r

r = ^(ln2)/₅₇₃₀

Now that we know what r is, we can simply solve for the time where f(t) = 0.897P₀.

0.897 = e^-rt.

t = ^-ln(0.897)/_r ≈ 898.6

Thus, the mummy is approximately 899 years old.