Question

Mr. Hibbard found a magic penny which doubles in value
every day. The expression .01 .2
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)
Mr. Hibbard substituted x = 2 into the
expression .01. 2² = 163.48
Mr. Hibbard substituted x = 2 into the
expression .01 .2.2 = 163.48
Mr. Hibbard substituted x = 14 into the
expression .01. 214 = 163.48
Mr. Hibbard substituted x = 14 into the
expression .01·2·14 = 163.48

Answer 1

To find out how Mr. Hibbard reached the conclusion that the penny had grown to $163.84 after two weeks, we need to analyze how the value of the penny changes over time based on how it doubles every day.

The expression should represent the value of the penny in dollars, starting from $0.01 (the value of the penny) and doubling every day. Therefore, the correct expression is:

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

Where \( x \) is the number of days since Mr. Hibbard found the penny.

If Mr. Hibbard found the penny and then waited for 14 days (2 weeks):

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

We can calculate:

1. Calculate \( 2^{14} \):
- \( 2^{14} = 16384 \)

2. Now substitute this back into the expression:
- \( \text{Value} = 0.01 \cdot 16384 = 163.84 \)

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

So, the correct statement is:

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