# exponential growth function

• Aug 26th 2008, 02:34 PM
student4200
exponential growth function
I dont know if this is the right place for this thread.

1.) A picture supposedly painted by Vermeer (1632-1675) contains 99.5% of its carbon-14 (half-life 5730 yrs) From this information decide whether the picture is a fake. Explain reasoning.

I know the equation for exponential growth/half life stuff is P=(Po)(e^kt)

I dont know where to go from there.
• Aug 26th 2008, 02:40 PM
Chris L T521
Quote:

Originally Posted by student4200
I dont know if this is the right place for this thread.

1.) A picture supposedly painted by Vermeer (1632-1675) contains 99.5% of its carbon-14 (half-life 5730 yrs) From this information decide whether the picture is a fake. Explain reasoning.

I know the equation for exponential growth/half life stuff is P=(Po)(e^kt)

I dont know where to go from there.

Note that $\displaystyle \frac{P}{P_0}=.995$

Then find k: $\displaystyle \lambda=\frac{\ln(2)}{k}\implies k=\frac{\ln(2)}{\lambda}$, where $\displaystyle \lambda$ is the half-life.

Note that since we're dealing with decay, the equation would have the form $\displaystyle P=P_0e^{{\color{red}-}kt}$

Once you find k, substitute this into your equation:

$\displaystyle .995=e^{-kt}$

Then solve for t.

Does this make sense?

--Chris
• Aug 27th 2008, 07:58 AM
mr fantastic
Quote:

Originally Posted by student4200
I dont know if this is the right place for this thread.

1.) A picture supposedly painted by Vermeer (1632-1675) contains 99.5% of its carbon-14 (half-life 5730 yrs) From this information decide whether the picture is a fake. Explain reasoning.

I know the equation for exponential growth/half life stuff is P=(Po)(e^kt)

I dont know where to go from there.

If probability and/or statistics was at all relevant to your question then this would be the right place to post this question .......