Question

Given the function h(x) = 4^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Part A: Find the average rate of change of each section. (4 points)

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points) Please Help Me

Answer 1

A) average rate=Δy/Δx=(y2-y1)/(x2-x1)=(h2-h1)/(x2-x1)
from x1 = 0 to x2= 1, h(x) = 4^x, h(0)=4^0=1, h(1)=4^1=4
average rate=(h2-h1)/(x2-x1)=(4-1)/(1-0)=3 (section A for interval x=0 to x=1)
from x1 = 2 to x2= 3, h(x) = 4^x, h(0)=4^2=16, h(1)=4^3=64
average rate=(h2-h1)/(x2-x1)=(64-16)/(3-2)=48 (section B for interval x=2 to x=3)
B) av.rate section B/ av. rate section A=48/4=12
this is exponential function, and for Δx=1, Δy change more for bigger numbers