1. **State the problem:** You earn a wage that doubles every day starting from 0.01 on day 1, 0.02 on day 2, 0.04 on day 3, and so on. We want to find the total income after working 31 days. 2. **Formula used:** This is a geometric series where the first term $a = 0.01$ and the common ratio $r = 2$. 3. **Sum of geometric series:** The total income $S_n$ after $n$ days is given by: $$ S_n = a \frac{r^n - 1}{r - 1} $$ 4. **Apply values:** For $n=31$, $a=0.01$, and $r=2$: $$ S_{31} = 0.01 \frac{2^{31} - 1}{2 - 1} = 0.01 (2^{31} - 1) $$ 5. **Calculate $2^{31}$:** $$ 2^{31} = 2147483648 $$ 6. **Calculate total income:** $$ S_{31} = 0.01 (2147483648 - 1) = 0.01 \times 2147483647 = 21474836.47 $$ **Final answer:** Your total income after 31 days is **21474836.47**.