Answer
a) $P=3.2(1.02)^t$, 23.183, (ii) $P=3.2 e^{0.02 t}$, $23.645$
b) ii) grows faster.
Work Step by Step
(a) (i) The population, $P$, in millions, is given by $P=3.2(1.02)^t$, so a century later
$$
P=3.2(1.02)^{100}=23.183 \text { million. }
$$
(ii) The population, $P$, in millions, is given by $P=3.2 e^{0.02 t}$, so a century later
$$
P=3.2 e^{0.02(100)}=23.645 \text { million. }
$$
(b) Since $e^{0.02}=1.0202 \ldots$ the growth factor in part (ii) is larger than the growth factor of 1.02 in part (i). We expect the answer to part (ii) to be larger.
