Question

The amount of carbon-14 in animal bones after t years is given by P(t)=P[0]e^(-0.00012097t). A bone has lost 37% of its carbon-14. How old is the bone?

Answer 1

To find the age of the bone, we need to solve the exponential equation
`P(t) = P[0]e^{(-0.00012097t)` for t when the bone has lost 37% of its carbon-14. By plugging in 0.63P[0] for P(t) and solving the resulting equation, we find that the bone is approximately 5,732.9 years old.

Step-by-step explanation:

To find the age of the bone, we need to solve the equation
`P(t) = P[0]e^{(-0.00012097t)` for t when the bone has lost 37% of its carbon-14. We can represent this as 0.63P[0] since the bone has lost 37%. Plugging this into the equation, we get
`0.63P[0] = P[0]e^{(-0.00012097t)`. We can cancel P[0] and divide both sides by 0.63 to get
`e^((-0.00012097t)) = 0.63`. Taking the natural logarithm of both sides, we have -0.00012097t = ln(0.63). Solving for t, we find that t ≈ 5,732.9 years. Therefore, the bone is approximately 5,732.9 years old.

Answer 2

63 years :) Hope this helps ;D