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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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01:24
Jeffrey Payo
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 4
Exponential Functions
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Johns Hopkins University
Missouri State University
Harvey Mudd College
Baylor University
Lectures
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A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
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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
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