WEBVTT
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Write an exponential equation in the form 𝑦 is equal to 𝑏 to the power of 𝑥 for the numbers in the table.
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We are given four sets of values.
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When 𝑥 equals zero, 𝑦 is equal to one.
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When 𝑥 equals one, 𝑦 is two-fifths.
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When 𝑥 equals two, 𝑦 is four over 25.
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And when 𝑥 equals three, 𝑦 is equal to eight over 125.
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We can calculate the value of 𝑏 in the equation by substituting in our values.
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We begin with 𝑥 equals zero and 𝑦 equals one.
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This gives us one is equal to 𝑏 to the power of zero.
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However, anything to the power zero is equal to one, so this does not help us calculate the value of 𝑏.
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Moving on to the second pair of values, we have two-fifths is equal to 𝑏 to the power of one.
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Anything to the power of one is itself.
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Therefore, 𝑏 is equal to two-fifths.
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Substituting this back into our equation gives us 𝑦 is equal to two-fifths to the power of 𝑥.
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We can then check this answer by substituting in our third and fourth pair of values.
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When 𝑥 equals two and 𝑦 is four twenty-fifths or four over 25, we have four over 25 is equal to two-fifths squared.
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When squaring a fraction, we can square the numerator and denominator separately.
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Two squared is equal to four, and five squared is 25.
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This means that the formula is correct for this pair of values.
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Finally, we have eight over 125 is equal to two-fifths cubed.
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Once again, we can split the numerator and denominator.
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So we have two cubed over five cubed.
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Two cubed is equal to eight, and five cubed is 125.
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Therefore, this pair of values is also correct.
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The exponential equation for the numbers in the table is 𝑦 is equal to two-fifths to the power of 𝑥.