I could prove this through writing the exponential equation that resembles this equation, but it's simpler than that:
It mentions that the population would be half of what it was before (a decade before). Now it is safe to say that every exponential (not decaying) equation gradually increases so that every value differs from it's consecutive value through multiplication of a constant.
<em>That is why, given the population would be half of what it was before, 0.5 acts as the 'constant' and the word problem can be modeled by an exponential graph + exponential function.</em>
