Modern whales appeared 5-10 million years ago. The vertebrae of a whale discovered by paleontologists contain roughly 0.25% as much carbon 14 as they would have

Question

Modern whales appeared 5-10 million years ago. The vertebrae of a whale discovered by paleontologists contain roughly 0.25% as much carbon 14 as they would have contained when the whale was alive. How long ago did the whale die? Use k=0.00012.

Answer 1

this is definitely a whale of a problem. Literally tons of fun.

using an exponential decay equation

with t = number of years, k= decay rate, e= about 2.71828...

A = Aoe^-kt

.25 = e^.-00012t

ln.25 = -.00012t

t = ln.25/-.00012 = 1.386294361/.00012= = about 11,552 years old or about 9,352 B.C.

half life for carbon dating is about 5,730. .25 is 1/2 of 1/2 or 2 half lives

or 2 x 57300 = 11,460 years which is close to 11,552.

since carbon dating is not reliable for over 30,000 years, you'll never have a whale a million years old using carbon dating. Usual date for evolution of modern whales is about 50 million years ago, after dinosaurs went extinct, but before humans appeared. They aren't fish, they're mammals, warm blooded, breathing air with lungs. No gills, so they can't breathe under water. Fish fins evolved into feet as fish crawled onto land, then the biggest hugest warm blooded land mammals crawled back into the cold ocean, lost their legs and got fins back? Yet there are no fossils showing this odd transition. same with dolphins and other fish like mammals