The number of households with cable TV service in a certain community, $N$, begins at only $45$ households and has seen a fivefold increase every $15$ years. Give the constants $a$, $b$, and $T$ so that $N$ is represented by a function of the form $N = ab^{t/T}$, where $t$ is the time in years since $N$ was first measured.

$a =$ help (numbers)
$b =$ help (numbers)
$T =$ help (numbers)