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Identify the dependent variable in the following situation: Ethan spent π dollars on π pens.
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a) The number of dollars, π or b) the number of pens, π.
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Letβs think about this situation in terms of input and output.
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In this machine, we have an input that we put in, a rule that somehow changes what weβve put in, and outcomes, the output.
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The input here represents the independent variable, and the output represents the dependent variable, because the output depends on the rule.
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We can use this machine to model our situation.
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What is the rule here?
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What is changing?
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We calculate the money based on the price of the pens.
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The number of pens, π, goes into our machine.
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We calculate the price per pen, and out comes the number of dollars Ethan needs to spend, π.
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The dollars Ethan spends depends on the price of the pens and the number of pens he buys.
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We were interested in the dependent variable, and that would be option a), the number of dollars, π.
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The number of dollars depends on the number of pens and the price of those pens.