Question

(Exponential decay)

"It is known that for the radioactive decay of carbon-14, the time it takes to decay to one half of its original mass is 5000 years. A sample of early humanoid remains contains 10% of its original mass of carbon-14. Determine the start of civilization as we know it if carbon-14 decays according to the equation: dM/dt = kM."

Answer 1

I'm a bit lost due to the lack of values given.

Answer 2

you goofed a little...

when t = 5000, \[M = \frac{M_0}{2}\] so you get \[\frac{1}{2} = e^{-5000k}\] and solve for k.

Answer 3

Oh dear, haha. Thanks for that, I'll have another go at it now and see how I go.

Answer 4

yeah, you got most of it and i'm sure you'll nail it!

Answer 5

Where'd you get the negative sign on 5000k?

Answer 6

sorry, just kinda habit since it's decay. you can leave it out and then find that k will be negative. if you leave it in then k will be positive. doesn't matter if you remember it's decay as opposed to growth.

Answer 7

Ohh, I see!

Answer 8

how do they know the original mass of the C14 in the sample? they must since they know they now have 10% of that remaining.

Answer 9

How does this look? It seems okay to me.

Answer 10

looks alright!

Answer 11

Awesome! Thanks mate. :)

Answer 12

you're welcome! Aussie?

Answer 13

Yep!

Answer 14

Was there in 2010... Brisbane, Sydney and even a road trip to Longreach from Brisbane.

Answer 15

That's pretty awesome, sounds like fun. :)