Situation:Find the age of the skull to the nearest year,Enter the correct answer.A hiker in Africa discovers a skull thatcontains 32% of its original amount of C-14.DONEN = Noekt00000No = inital amount of C-14 (at timet = 0)N = amount of C-14 at time tK = 0.0001t = time, in years

Answer:11,394  years oldStep-by-step explanation:The equation looks like this:[tex]N=N_{0}e^{kt}[/tex]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:[tex]100=32e^{.0001t}[/tex]Divide both sides by 32 to get[tex]3.125=e^{.0001t}[/tex]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) = .0001tDivide both sides by .0001 to get thatt = 11,394 years