For this case we have the following function:
[tex]S (t) = 3405.120e^{0.284t}[/tex]
By definition, the average rate of change is given by:
[tex]Avr =\frac{S(t2) -S(t1)}{t2-t1}[/tex]
If t is the number of years since 2000, we have to:
For the year 2001 [tex]t1 = 1[/tex]
For the year 2010 [tex]t2 = 10[/tex]
On the other hand:
[tex]S (t2) = 3405.120e^{0.284*10}\\S (t2) = 3405.120e^{2.84}\\S (t2) = 58281[/tex]
While:
[tex]S (t1) = 3405.120e^{0.284*1}\\ S (t1) = 3405.120e^{0.284}\\S (t1) = 4524[/tex]
So, we have to:
[tex]Avr =\frac{58281-4524}{10-1}[/tex]
[tex]Avr =\frac{53757}{9}\\Avr = 5973[/tex]
So, the average rate of change is given by: 5973
Answer:
[tex]Avr =5973\frac{millions-of-dollars}{year}[/tex]
