Question

mr hibbard found a magic penny which doubles in value every day the expression .01 • 2^x where x is the number days since mr hibbard found the penny
mr hibbard realized after just 2 weeks the penny had becomr $163.84 how did he reach this solution

Answer 1

To understand how Mr. Hibbard reached the value of $163.84 after 2 weeks with the magic penny that doubles in value every day, we can break it down mathematically using the expression \(0.01 \times 2^x\), where \(x\) is the number of days since he found the penny.

### Step-by-step Calculation:

1. **Determine the Number of Days:**
Mr. Hibbard realized after just 2 weeks. Since there are 14 days in 2 weeks, we set \(x = 14\).

2. **Substitute \(x\) into the Expression:**
Using the expression \(0.01 \times 2^x\), we substitute \(x\) with 14:
\[
\text{Value after 14 days} = 0.01 \times 2^{14}
\]

3. **Calculate \(2^{14}\):**
First, we need to compute \(2^{14}\):
- \(2^{10} = 1024\)
- Therefore, \(2^{14} = 2^{10} \times 2^4 = 1024 \times 16 = 16384\).

4. **Multiply by 0.01:**
Now, we multiply this result by \(0.01\):
\[
0.01 \times 16384 = 163.84
\]

### Conclusion:
So, after 14 days, the penny had indeed become $163.84. Mr. Hibbard used the expression correctly to reach this solution:

\[ \text{Value} = 0.01 \times 2^{14} = 163.84 \]