Question 1136743:
Your boss offers you a ten-day job with three choices for how to be paid. Option #1 says that you will receive $1 the first day, $2 the second day, $3 the third day, and so on. Option #2 says you will receive 10₵ the first day, 20₵ the second day, 40₵ the third day, 80₵ the fourth day, and so on. Option #3 says that you will receive $6 a day for all ten days.which option should u choose if u want to make most amount of money?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! with option 1, you would get paid 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 dollars.
with option 2, you would get paid .1 + .2 + .4 + .8 + 1.6 + 3.2 + 6.4 + 12.8 + 25.6 + 51.2 = 102.3 dollars.
with option 3, you would get paid 6 * 10 = 60 dollars.
looks like option 2 needs to be your choice if you want to make the most money.
option 2 is a geometric series.
the formula is An = A1 * r ^ (n-1).
A1 is .1
r is 2 because it doubles every time.
n is 10.
the formula becomes A10 = .1 * 2 ^ 9 = 51.2.
that's what you make on the 10th day.
the sum of a geometric series is Sn = A1 * (1 - r^n) / (1 - r)
in this problem, that becomes S10 = .1 * (1 - 2^10) / (1 - 2) which becomes S10 = .1 * (-1023) / -1 which becomes -102.3 / -1 which 102.3.
that'w what we got above when we added each of the individual terms manually.
anyway, option 2 is your best bet.
you make the most money with that option.
all that doubling every day gets pretty big as the number of days gets larger.
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