Answer:
[tex] \displaystyle 702[/tex]
Step-by-step explanation:
we are given a exponential function
[tex] \displaystyle f(x) = {3}^{x + 1} - 22[/tex]
where x represents the number and f(x) represents the amount
we are also given that when x is 3 then f(x) is 59 likewise when x is 6 then f(x) is 2165
to figure out the average rate of change between 3 and 6 we can consider the average rate of change formula given by
[tex] \displaystyle m = \frac{ f(x)_ {2} - f(x)_{1} }{ x_{2} - x_{1} } [/tex]
substitute what we have:
[tex] \displaystyle m = \frac{ 2165 - 59 }{6 - 3 } [/tex]
simplify substitution:
[tex] \displaystyle m = \frac{2106 }{3 } [/tex]
simplify division:
[tex] \displaystyle m = 702[/tex]
hence, the average rate of change between 3 and 6 is 702
