Suppose you go to work at a company that pays $0.02 for the first day, $0.04 for the second day, $0.08 for the third day, and so on. If the daily wage keeps doubling, what would your total income be for working 29 days? Round your answer to two decimal places.
A) $5,368,709.12
B) $2,684,354.56
C) $10,737,418.22
D) $42,949,672.88
E) $21,474,836.44

Question

Suppose you go to work at a company that pays $0.02 for the first day, $0.04 for the second day, $0.08 for the third day, and so on. If the daily wage keeps doubling, what would your total income be for working 29 days? Round your answer to two decimal places. ​
A) $5,368,709.12
B) $2,684,354.56
C) $10,737,418.22
D) $42,949,672.88
E) $21,474,836.44

Quizplus · Accepted Answer

The total income for working 29 days, with the wage doubling each day, can be calculated using the formula for the sum of a geometric series: $S_n = a(1 - r^n) / (1 - r)$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = 0.02$, $r = 2$, and $n = 29$. The sum is $0.02(1 - 2^{29}) / (1 - 2) = 0.02(2^{29} - 1)$. This equals approximately $10,737,418.22, making option C correct.

Suppose You Go to Work at a Company That Pays