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Mr. Hibbard found a magic penny which doubles in value every day. The expression .01⋅2x can be used to find the value of his coin where x is the number of days since Mr. Hibbard found the penny. Mr. Hibbard realized after just 2 weeks the penny had become $163.84! How did he reach this solution (1 point) Responses Mr. Hibbard substituted x=2 into the expression .01⋅2⋅2=163.48 Mr. Hibbard substituted x=2 into the expression point 0 1 times 2 times 2 is equal to 163 point 4 8 Mr. Hibbard substituted x=2 into the expression .01⋅22=163.48 Mr. Hibbard substituted x=2 into the expression point 0 1 times 2 squared is equal to 163 point 4 8 Mr. Hibbard substituted x=14 into the expression .01⋅2⋅14=163.48 Mr. Hibbard substituted x=14 into the expression point 0 1 times 2 times 14 is equal to 163 point 4 8 Mr. Hibbard substituted x=14 into the expression .01⋅214=163.48

1 answer

To find the value of Mr. Hibbard's magic penny after 2 weeks (which is 14 days), he should substitute \( x = 14 \) into the expression \( 0.01 \cdot 2^x \).

The correct calculation is:

  1. Substitute \( x = 14 \) into the expression: \[ 0.01 \cdot 2^{14} \]

  2. Calculate \( 2^{14} \): \[ 2^{14} = 16384 \]

  3. Multiply by \( 0.01 \): \[ 0.01 \cdot 16384 = 163.84 \]

Thus, the correct response from the options provided is:

  • Mr. Hibbard substituted \( x=14 \) into the expression \( 0.01 \cdot 2^{14} = 163.84 \).

Note: The answer has a slight typographical error in the hundreds place ("163.48" instead of "163.84"). The calculation itself is correct, leading to the conclusion of \( 163.84 \).