If the original function gives the carbon 14 remaining as a function of the number of of years that have passed, what information does the inverse...

The decay function of the carbon-14 isotope is an
exponential function: N(t) = No*e^(- *t)

is the decay constant, N(t) is the number of carbon 14 atoms remaining at time t and No
is the number of carbon atoms at t = 0.

The inverse
function can be calculated in the following way:

N(t) =
No*e^(-*t)

=> N(t)/No =
e^(-*t)

=> ln[N(t)/No] =
ln[e^(-*t)]

=> ln[N(t)/No] =
(-*t)*ln e

=> ln[N(t)/No]/(-) =
t

The inverse function provides the number of
years that have passed if the carbon-14 remaining at a time t and the initial amount of
carbon 14 are known.