Question

Situation:

Answer 1

Answer:

11,394  years old

Step-by-step explanation:

The equation looks like this:

$N=N_{0}e^{kt}$

The only thing left up to us is to decide what value should go in for N.  Since we are told that 32% of the original amount is what the hiker finds, we are operating in percentages.  Before any decomposition took place, the amount of skull was 100%.  Filling in now we have:

$100=32e^{.0001t}$

Divide both sides by 32 to get

$3.125=e^{.0001t}$

In order to get that t out of the exponential position that it is currently in, we will take the natural log of both sides, since a natural log "undoes" an e (that is because the base of a natural log is e).  Taking the ln of both sides and utilizing that rule for natural logs and e's gives us:

ln(3.125) = .0001t

Divide both sides by .0001 to get that

t = 11,394 years