Question

QF Q5.) Use the exponential decay model for​ carbon-14 to estimate the age of the paintings.

Answer 1

In the given exponential decay model, we are solving for age of the painting in t years.

A represents the amount of carbon-14 at t.

$A_0$ represents the original amount of carbon-14. This would be 100%.

So plug in what we know and solve for t:

$30 = 100e^{-0.000121t}$

Divide both sides by 100:

$\frac{3}{10}=e^{-0.000121t}$

Cancel out the e by finding the natural logarithm of both sides:

$ln( \frac{3}{10})=-0.000121t$

Finally, divide both sides by -0.000121:

$t = \frac{ln( \frac{3}{10} )}{-0.000121}$

Now use a calculator to find t:

t =  9950.188

To the nearest integer, the answer is 9950 years.

Answer 2

A=A₀$e^{0.000121t}$
A/A₀=30%=0.3
0.3=$e^{0.000121t}$
0.000121t=ln(0.3)
t=ln(0.3)/0.000121
=-9950.19
so painting is 9950 years old