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

Answer 1

Answer:

$ 10,737,418.23

Explanation:

Given:

Amount paid on the first day = $ 0.02

Amount paid on the Second day = $ 0.04

Amount paid on the third day = $ 0.08

number of days, n = 29

also,

the wages is doubling daily

therefore,

The total of the wages for 29 days will be = $ 0.02 + $ 0.04 + $ 0.08 + ....

or we can form the relation as

= $ 0.02 × ( 2⁰ + 2¹ + 2² + 2³ + ........ )

or

= $\sum_{k=0}^{29}2^n$

or

= $0.01\times(2^{n+1}-1)$

or

= $0.01\times(2^{29+1}-1)$

or

= $ 10,737,418.23