Question

Mr. Hibbard found a magic penny which doubles in value every day. The expression .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=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=14 into the expression .01⋅214=163.48
Mr. Hibbard substituted x=14 into the expression point 0 1 times 2 to the 14th power 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

Answer 1

To find out how Mr. Hibbard reached the solution of $163.84 after 2 weeks (which is 14 days), we should look at the correct substitution into the expression \(0.01 \cdot 2^x\).

The expression \(0.01 \cdot 2^x\) represents the value of the penny after \(x\) days, starting from $0.01.

If Mr. Hibbard realizes after 2 weeks (14 days), he would need to substitute \(x=14\) into the expression:

\[
\text{Value} = 0.01 \cdot 2^{14}
\]

Now let's calculate \(2^{14}\):

\[
2^{14} = 16384
\]

Now multiplying by \(0.01\):

\[
0.01 \cdot 16384 = 163.84
\]

Therefore, Mr. Hibbard's understanding is correct when he substitutes \(x=14\) into the expression.

So the correct response is:

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