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

Answer 1

The expression \(0.01 \cdot 2^x\) represents the value of the magic penny in dollars after \(x\) days. Here's a breakdown of how it works:

- The \(0.01\) represents the initial value of the penny, which is 1 cent.
- The \(2^x\) part indicates that the value of the penny doubles every day.

So, for each day that passes (each increase in \(x\) by 1), the value of the penny multiplies by 2.

To find the value of the penny after a certain number of days, you simply substitute the number of days into the expression for \(x\):

- If \(x = 0\) (the day he found the penny), the value is:
\[
0.01 \cdot 2^0 = 0.01 \cdot 1 = 0.01 \text{ dollars (1 cent)}
\]

- If \(x = 1\) (1 day later), the value is:
\[
0.01 \cdot 2^1 = 0.01 \cdot 2 = 0.02 \text{ dollars (2 cents)}
\]

- If \(x = 2\) (2 days later), the value is:
\[
0.01 \cdot 2^2 = 0.01 \cdot 4 = 0.04 \text{ dollars (4 cents)}
\]

- If \(x = 10\) (10 days later), the value is:
\[
0.01 \cdot 2^{10} = 0.01 \cdot 1024 = 10.24 \text{ dollars}
\]

You can calculate the value for any day by substituting the corresponding value of \(x\) into the expression.