Question

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

Answer 1

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

Answer 2

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:


`(3)/(10)=e^(-0.000121t)`

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


`ln( (3)/(10))=-0.000121t`

Finally, divide both sides by -0.000121:


`t = (ln( (3)/(10) ))/(-0.000121)`

Now use a calculator to find t:

t = 9950.188

To the nearest integer, the answer is 9950 years.