Suppose you go to a company that pays $\mathrm{\$}0.03$ for the first day, $\mathrm{\$}0.06$ for the second day, $\mathrm{\$}0.12$ 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 $=\mathrm{\$}$
Question Help: $◻$ Video $◻$ Message instructor
Submit Question

Step 1 ：Suppose you go to a company that pays $0.03forthefirstday,$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 $\boxed{{\displaystyle 64424509.41}}$ dollars.