# 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 function provide?

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justaguide | Certified Educator

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

`lambda` 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^(-`lambda`*t)

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

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

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

=> ln[N(t)/No]/(-`lambda`) = 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.**