Answer
Time logarithmically grows with the population.
Work Step by Step
If the population growth is modeled by $P=Ab^{t}$
we express $t$ as a function of $P$ (solve for P):
$P/A=b^{t}$
$\log_{b}(P/A)=\log_{b}b^{t}$
Apply
$\displaystyle \log_{b}\left(\frac{x}{y}\right)=\log_{b}x-\log_{b}y$
and
$\log_{b}\left(b^{x}\right)=x$
We get:
$t=\log_{b}P-\log_{b}A$
which is of the form
$t=\log_{b}P+C$
and this is a logarithmic growth.
Thus, time logarithmically grows with population.
