Respuesta :
Answer:
The average rate of change is 3.
Step-by-step explanation:
The given points are
[tex](1, 2)\\(2,4)\\(3,8)\\(4,16)\\(5,32)\\(6,64)[/tex]
Notice that the relation between coordinates is exponential, because y-values are the result of a power with base 2, and x-values represents exponents.
The function that defines this sequence is
[tex]f(x)=2^{x}[/tex]
Where the factor that creates this geometric sequence is 2.
However, when we talk about the average rate of change, it's defined as
[tex]r=\frac{\Delta y}{\Delta x}[/tex]
In words, it's the quotient between the change of vertical values and the change of horizontal values.
In this case, we have
[tex]r=\frac{8-2}{3-1}=\frac{6}{2}=3[/tex]
Therefore, the average rate of change from n = 1 to n = 3 is 3.
