ANSWER
B. 39,366
EXPLANATION
The y-values of the exponential function has the following pattern
[tex] {3}^{0} = 1[/tex]
[tex] {3}^{1} = 3[/tex]
[tex] {3}^{2} = 9[/tex]
[tex] {3}^{3} = 27[/tex]
:
:
[tex] {3}^{x} = y [/tex]
Or
[tex]f(x) = {3}^{x} [/tex]
To find the average rate of change from x=9 to x=10, we simply find the slope of the secant line joining (9,f(9)) and (10,f(10))
This implies that,
[tex]slope = \frac{f(10) - f(9)}{10 - 9} [/tex]
[tex]slope = \frac{ {3}^{10} - {3}^{9} }{1} [/tex]
[tex]slope = \frac{59049-19683}{1} = 39366[/tex]
Therefore the average rate of change from x=9 to x=10 is 39366.
The correct answer is B.
