Question

The proportion of carbon-14 still present in a sample after t years is e−⁰.⁰⁰⁰¹²ᵗ . Estimate the age of cave paintings if the carbon with which they were drawn contains only 2.3% of its original carbon-14.

Answer 1

To estimate the age of the cave paintings, we can use the proportion of carbon-14 still present in the carbon used to draw them. The proportion of carbon-14 after t years is given by the equation e^-0.000012t. We can set up an equation and solve for t to estimate the age of the cave paintings.

Step-by-step explanation:

To estimate the age of the cave paintings, we can use the proportion of carbon-14 still present in the carbon used to draw them. The proportion of carbon-14 after t years is given by the equation e-0.000012t. We are told that the carbon used for the drawings contains only 2.3% of its original carbon-14. We can set up an equation and solve for t to estimate the age of the cave paintings.

2.3% = 100% * e-0.000012t

To solve for t, we can take the natural logarithm of both sides of the equation:

ln(2.3%) = -0.000012t

t ≈ ln(2.3%) / -0.000012