Suppose you go to a company that pays $\$ 0.03$ for the first day, $\$ 0.06$ for the second day, $\$ 0.12$ for the third day, and so on. If the daily wage keeps doubling, what will your total income be for working 31 days? Total Income $=\$$ Question Help: $\square$ Video $\square$ Message instructor Submit Question

Step 1 ：Suppose you go to a company that pays $0.03 for the first day, $0.06 for the second day, $0.12 for the third day, and so on. If the daily wage keeps doubling, what will your total income be for working 31 days?

Step 2 ：We can solve this problem by using the formula for the sum of a geometric progression. The first term \(a\) is $0.03, the common ratio \(r\) is 2, and the number of terms \(n\) is 31.

Step 3 ：The formula for the sum \(S\) of a geometric progression is \(S = a \cdot \frac{r^n - 1}{r - 1}\).

Step 4 ：Substituting the given values into the formula, we get \(S = 0.03 \cdot \frac{2^{31} - 1}{2 - 1}\).

Step 5 ：Calculating the above expression, we find that the total income for working 31 days will be \(\boxed{64424509.41}\) dollars.