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Numerade Educator

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Problem 10 Easy Difficulty

Graph the given functions on a common screen. How are these graphs related?

$ y = 0.9^x $ , $ y = 0.6^x $ , $ y = 0.3^x $ , $ y = 0.1^x $

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Video Transcript

in this problem, we're going to use a graphing calculator to compare some different graphs on a common screen and see how they're related. So we go toe y equals and we type the four functions in there. And what we see is each one has a base that's between zero and one. And so let's see how changing that base affects the graph. For my viewing window. I'm using negative 10 to 10 on the X axis and negative 2 to 20 on my Y axis. But those numbers could be different. You could just fiddle with it until you find something you like. So now we look at the graphs. Now the blue one is y equals 10.9 to the X. The red one is y equals 10.6 to the X. The black one is y equals 10.3 to the X, and the pink one is y equals 10.1 to the X. Notice that the closer the base is toe one, the less steep the graph is. The steepest of the graphs had the base that was closest toe one are closest to zero, and the let least steep had the base that was, uh, closest to one. Other than that, they are all exponential decay graphs