The model would take the form of
\(P(t)=P(0)e^{0.035t}\)
So in 2015, when \(t=15\), the population would be
\(P(15)=43230e^{0.035\times15}\approx73079\)
On the other hand, you could use the following discrete model for the population, which gives a similar result. If \(t=0\) corresponds to the year 2000, then in 2001, when \(t=1\), you have
\(P(1)=P(0)\times1.035^1\approx44743\)
In the next year,
\(P(2)=P(1)\times1.035^1=P(0)\times1.035^2\approx46309\)
And so on, making the general pattern for the \(t\)th year to be
\(P(t)=P(t-1)\times1.035^1=P(t-2)\times1.035^2=\cdots=P(0)\times1.035^t\)
This means in the year 2015, or when \(t=15\), the population should be approximately
\(P(15)=P(0)\times1.035^{15}\approx72425\)
