Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.
The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not.
The number $c$ in the exponential measures the exponential rate of decay of Carbon $.
Carbon 14 is a form of carbon which decays exponentially over time.
The two solutions provided differ slightly in their approach in this regard.
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The carbon-14 undergoes radioactive decay once the plant or animal dies, and measuring the amount of carbon-14 in a sample conveys information about when the plant or animal died.
In this tutorial I will step you through how to solve problems that deal in exponential growth and decay.