Question

A human skeleton is found in an archeological dig. Carbon dating is implemented to determine how old the skeleton is by using the equation y= e^-0.0001210t , where y is the percent of radiocarbon remaining when the skeleton is t years old.

Find the inverse of the carbon dating equation. What does it mean?

My answer:
y=e^rt
r=-0.0001210
t= Age of sample


Can someone please help me check my work. I’m not sure if I’m completely right. I feel like I’m missing something or doing this wrong.

Answer 1

the inverse function for
y= e^-0.0001210t
found via
ln y = -0.0001210t
lny/-0.0001210 = t
so y^{^-1}(t) = -1/0.0001210 ln(t) = -8264.46 ln(t)