Question

Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about - the amount found in living human beings. The amount of carbon-14 present in animal bones after t years is given by y, where is the amount of carbon-14 present in living human beings. About how long ago did the Egyptian die?

Answer 1

we have the equation

$y=y_0e^{(-0.0001216t)}$

In this problem, we know that

$y=\frac{2}{7}y_0$

substitute in the given equation and solve for t

so

$\frac{2}{7}y_0=y_0e^{(-0.000121,6t)}$

simplify

$\frac{2}{7}=e^{(-0.000121,6t)}$

Apply ln on both sides

$\begin{gathered} ln\frac{2}{7}=lne^{(-0.000121,6t)} \\ ln\frac{2}{7}=-0.0001216t \end{gathered}$

t=10,302 years