# Math Help - exponential growth function

1. ## 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.

2. 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 $\frac{P}{P_0}=.995$

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

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

Once you find k, substitute this into your equation:

$.995=e^{-kt}$

Then solve for t.

Does this make sense?

--Chris

3. 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 .......