Answer
A) Clearly, an exponential function would be most suitable.
B) $
P(t)=20,000(1.0414)^t
$
Work Step by Step
A) Let $P_0= 20000$ be the initial population and that it increases by $4.14\%$ per year, the balance population after one year is
A general formula of the population can be expressed as
$$
P=P_0+0.0414P_0 t
$$
The population in 2010 would be
$$
P=2000+0.0414(20000) \cdot 10= 28280
$$
If the population increases exponentially, the population in 2010
$$
P=2000(1.0414)^{10}=30,006.
$$
Clearly, an exponential function would be most suitable.
B) An exponential function of the population is
$$
P(t)=20,000(1.0414)^t
$$
