1. Carbon-14 is a radioactive isotope of the element carbon.

Carbon-14 decays exponentially – as it decays it loses mass.

Carbon-14 is used in carbon dating to estimate the age of objects.

The time it takes the mass of carbon-14 to halve (called its half-life) is approximately 5700 years

 A model for the mass of carbon-14, $y$ g, in an object originally containing 100 g, at time $t$ years is

$y=100{e}^{-kt}$

where $k$ is a constant.

Find the value of $k$, giving your answer to three significant figures.