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=(2)/(7)y_0`

substitute in the given equation and solve for t

so

`(2)/(7)y_0=y_0e^((-0.000121,6t))`

simplify

`(2)/(7)=e^((-0.000121,6t))`

Apply ln on both sides

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

t=10,302 years