Step 1 :Given a company that pays $0.01 for the first day, $0.02 for the second day, $0.04 for the third day and so on, with the daily wage doubling each day, we are asked to find the total income for working 30 days.
Step 2 :This problem can be solved as a geometric progression problem where the first term (a) is $0.01, the common ratio (r) is 2, and the number of terms (n) is 30.
Step 3 :The sum (S) of a geometric progression can be calculated using the formula: \(S = a \times \frac{r^n - 1}{r - 1}\)
Step 4 :Substituting the given values into the formula, we get: \(S = 0.01 \times \frac{2^{30} - 1}{2 - 1}\)
Step 5 :Solving the equation gives us the total income for working 30 days.
Step 6 :Final Answer: \(\boxed{10737418.23}\)