Question

What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?

Answer 1

Average rate of change refers to the slope of a function/equation. 
To solve this, plug in for both x values and calculate the average, or mean. 

x = 1 
f(1) = 5(2)^1 
      = 5(2) 
      = 10

x = 5 
f(5) = 5(2)^5
      = 5(32) 
      = 160

Now, you calculate the average: 
10 + 160 = 170 
Divide by 2 and you get 85.