Answer
Makes sense.
Work Step by Step
Exponential growth and decay models are given by $A=A_{0}e^{kt}$
in which $t$ represents time,
$A_{0}$ is the amount present at $t=0$, and
$A$ is the amount present at time $t$.
If $k > 0$, the model describes growth and $k$ is the growth rate.
If $k < 0$, the model describes decay and $k$ is the decay rate.
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Fossils are remains of an organic (live at one time in the past) entity.
We assume that at the time of death,
the amount (ratio, or percentage) of radioactive carbon-14 in the entity would be close to the ratio (percentage) if it died today.
In the fossil remains, however, the C-14 decayed to an amount $A$, less than the initial $A_{0}$, and since we know the decay rate for C-14, we solve
$A=A_{0}e^{kt}$ for t,
giving us an approximation of time lapsed.
