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