Question

Mr. Hibbard found a magic penny which doubles in value every day. The expression .01⋅2x.01⋅2x 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 = 14 into the expression .01⋅2⋅14=163.48.01⋅2⋅14=163.48Mr. 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 = 2 into the expression .01⋅2⋅2=163.48.01⋅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=163.48.01⋅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⋅214=163.48

Answer 1

To understand how Mr. Hibbard reached the solution, we need to analyze the expression given and the value after 14 days.

The expression .01⋅2^x represents the value of the penny after x days, starting from an initial value of $0.01 and doubling every day.

After 14 days, substituting \( x = 14 \) into the expression:

\[ 0.01 \cdot 2^{14} \]

Now we need to calculate \( 2^{14} \):

\[ 2^{14} = 16384 \]

Now, substituting that value back into the expression:

\[ 0.01 \cdot 16384 = 163.84 \]

So, Mr. Hibbard indeed substituted \( x = 14 \) into the expression \( 0.01 \cdot 2^{14} \) to get $163.84.

The correct response from the options given would be:

Mr. Hibbard substituted x = 14 into the expression .01⋅2^14 = 163.84.