Question

Whta is the average e of change for this exponential function for the interval from x=1 to x= 3?

Answer 1

In this context:

`\boxed{ARC=3}`

Step-by-step explanation:

Hello! Remember you have to write complete questions in order to get good and exact answers. Here, I'll assume the exponential function is:

`f(x)=2^x`

Every exponential function is a nonlinear function, and remember for any nonlinear function the slope changes at each point, so the average rate of change between any two points
`(x_(1),f(x_(1)) \ and \ (x_(2),f(x_(2))` is the slope of the line through the two points:

`ARC=(f(x_(2))-f(x_(1)))/(x_(2)-x_(1)) =(Change \ in \ y)/(Change \ in \ x)`

Here we set:

`x_(1)=x=1 \\ \\ x_(2)=x=3 \\ \\ \\ So: \\ \\ f(x_(1))=2^1=2 \\ \\ f(x_(3))=2^3=8 \\ \\ \\ ARC=(8-2)/(3-1) \\ \\ \boxed{ARC=3}`