﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.17,0:00:07.03,Default,,0000,0000,0000,,Here we have two pretty simple exponential functions. Two to the power of X and three to the power of X. Dialogue: 0,0:00:07.03,0:00:15.37,Default,,0000,0000,0000,,Two to the power of zero is one; three to the power of zero is one; two to the power of one is two. Dialogue: 0,0:00:15.37,0:00:23.77,Default,,0000,0000,0000,,Two to the power of two is four. Two to the power of minus one equals one over two, one half, and so on. Dialogue: 0,0:00:23.77,0:00:30.77,Default,,0000,0000,0000,,Three to the power of one equals three. Three to the power of two gets pretty big--nine. Dialogue: 0,0:00:30.77,0:00:37.20,Default,,0000,0000,0000,,Three to the power of minus one, one over three, one-third, and so on, and so on. Dialogue: 0,0:00:37.20,0:00:43.07,Default,,0000,0000,0000,,Here comes a quiz for you: What's the slope of the tangent line at X equals zero? Dialogue: 0,0:00:43.07,0:00:50.47,Default,,0000,0000,0000,,Is the slope larger than one? Is it equal to one, or is it smaller than one? Dialogue: 0,0:00:50.47,0:00:54.97,Default,,0000,0000,0000,,In both cases, look at the tangent lines--what would you say?