Answer:
The average rate of change between 2003 and 2011 is 147.638
Step-by-step explanation:
We are given the following population model:
Population model:
[tex]P(t) = 1500e^{0.06t}[/tex]
where t is the years after the start of the year 2000.
Population in 2003 =
[tex]P(3) = 1500e^{0.06(3)}\\P(3) \approx 1795.83[/tex]
Population in 2013 =
[tex]P(13) = 1500e^{0.06(13)}\\P(13) \approx 3272.21[/tex]
Average rate of change of the population between 2003 and 2013:
[tex]\dfrac{P(b)-P(a)}{b-a}\\\\=\dfrac{P(13)-P(3)}{13-3}\\\\=\dfrac{3272.21-1795.83}{13-3}\\\\\approx 147.638[/tex]
Thus, average rate of change between 2003 and 2011 is 147.638
