Answer:
[tex]Average = 30[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4^{x - 1} + 2[/tex]
Required
Average [tex]rate\ of\ change[/tex] from 2 to 4
This is calculated using:
[tex]Average = \frac{f(b) - f(a)}{b - a}[/tex]
Where
[tex]a= 2[/tex] and [tex]b = 4[/tex]
So:
[tex]Average = \frac{f(4) -f(2)}{4 - 2}[/tex]
[tex]Average = \frac{f(4) -f(2)}{2}[/tex]
Calculate f(2) and f(4)
[tex]f(x) = 4^{x - 1} + 2[/tex]
[tex]f(2) = 4^{2-1} + 2[/tex]
[tex]f(2) = 4 + 2[/tex]
[tex]f(2) = 6[/tex]
[tex]f(4) = 4^{4-1} + 2[/tex]
[tex]f(4) = 4^3 + 2[/tex]
[tex]f(4) = 66[/tex]
So:
[tex]Average = \frac{f(4) -f(2)}{2}[/tex]
[tex]Average = \frac{66 - 6}{2}[/tex]
[tex]Average = \frac{60}{2}[/tex]
[tex]Average = 30[/tex]
