The number of bacteria in a strain is given by $B(t) = 30e^{1.5t}$, where $t$ is the time in hours.
a) How many bacteria are there at time zero?
b) How long will it take the number of bacteria to double?
a) $30e^{1.5t} = 30e^0 = 30$
b) $30e^{1.5t} \ge 2$
$\implies e^{1.5t} = \frac{1}{15}$
$\implies 1.5t = \ln(\frac{1}{15})$
This gives a minus number.
a) okay : $30~e^{1.5~(0)}=30$
b) You want the time when this is doubled: $30 \, e^{1.5 t}=60~$
$$t = \dfrac{\ln 2}{1.5} $$