Mathematics: Can someone pls help me on this one

Can someone pls help me on this one

FlyingUnicorn123

09.06.2023

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:

$P(t) = 1500e^{0.06t}$

where t is the years after the start of the year 2000.

Population in 2003 =

$P(3) = 1500e^{0.06(3)}\\P(3) \approx 1795.83$

Population in 2013 =

$P(13) = 1500e^{0.06(13)}\\P(13) \approx 3272.21$

Average rate of change of the population between 2003 and 2013:

$\dfrac{P(b)-P(a)}{b-a}\\\\=\dfrac{P(13)-P(3)}{13-3}\\\\=\dfrac{3272.21-1795.83}{13-3}\\\\\approx 147.638$

Thus, average rate of change between 2003 and 2011 is 147.638

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