Question

Anybody have any clue how to do this:

This exercise uses the radioactive decay model.

A wooden artifact from an ancient tomb contains 65% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)
________yr

Answer 1

yeah we can do this

Answer 2

put
\[.65=(\frac{1}{2})^{\frac{t}{5700}}\] and solve for t

Answer 3

you get
\[\frac{t}{5700}=\frac{\ln(.65)}{\ln(\frac{1}{2})}\] by the change of base formula

Answer 4

so
\[t=\frac{5700\times \ln(.65)}{\ln(.5)}\]

Answer 5

3542?

Answer 6

i put it in a calculator and get 3542 rounded

Answer 7

yup!