Mr. Hibbard found a magic penny which doubles in value every day. The expression .01⋅2x

Question

where x is the number of days since Mr. Hibbard found the penny.



Mr. Hibbard realized after just 14 days, 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

Answer 1

To find the value of the penny after 14 days, Mr. Hibbard would use the expression \(0.01 \cdot 2^x\), where \(x\) is the number of days since he found the penny.

Since he wants to find the value after 14 days, he would substitute \(x = 14\) into the expression:

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

Now, calculating \(2^{14}\):

\[ 2^{14} = 16384 \]

Then, multiply this by \(0.01\):

\[ 0.01 \cdot 16384 = 163.84 \]

This computation shows that the penny is worth $163.84 after 14 days.

The correct response that reflects this calculation is:

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

(Note: The response has a typo showing \(163.48\); it should be \(163.84\) in the explanation.)