Answer
a) $271.83$
b) $28.40\%$ per hour
Work Step by Step
(a) Since the population of the bacteria is growing by a constant continuous percent rate, the function can be modelled as an exponential function, $a=100$ and $b=0.25$.
$$
P=100 e^{0.25t}
$$
The bacteria colony after 4 hours is
$$
P=100 e^{0.25\cdot 4}= 271.83
$$
b) Rewrite the above function in the form: $P=a b^t$.
$$
P(t)=100\left(e^{0.25}\right)^t \approx 100(1.2840)^t
$$ From this, we see that $b=1.2840$. The population increases by about $28.40 \%$ per hour.
