Question

What is the average rate of change of the function

Answer 1

The average rate of change for this interval is expressed by the formula 

(y2 - y1) / (x2 - x1)

So use the endpoints at x=1 and x=5. The points are (5,160) and (1,10).
substitute in your values: (160-10)/(5-1). The answer is 150/4, or 37.5

Answer 2

The average rate of change of f(x) on the interval [a,b] is f(b)−f(a)/b−a.

We have that a=1, b=5, f(x)=5⋅2^x.

Thus, f(b)−f(a)/b−a = 5⋅2(5)−(5⋅2(1))/5−(1) = 75/2

Answer: The average rate of change is 75/2 = 37.5.

Hopefully this helps. 

~ ShadowXReaper069