Posted by **Lizzie** on Monday, May 7, 2012 at 2:16am.

In a financial deal, you are promised $800 the first day and each day after that you will receive 45% of the previous day's amount. When one day's amount drops below $1, you stop getting paid from that day on. What day is the first day you would receive no payment and what is your total income?

I am so confused about this problem. Could someone please show me the steps?

- Math -
**Anonymous**, Monday, May 7, 2012 at 2:31am
f(day)=800*.45^(day)

Set f(day)=1, solve for day by taking a log on both sides.

- Math -
**Anonymous**, Monday, May 7, 2012 at 2:31am
instead of .45^(day) you should actually use .45^(day-1) so that the first day is 800

- Math -
**Lizzie**, Monday, May 7, 2012 at 3:01am
I tried doing this, but I still have no idea how to solve this problem =/

- Math -
**Reiny**, Monday, May 7, 2012 at 8:37am
e.g.

day 1 = 800

day 2 = 800(.45)

day 3 = 800(.45)^2

looks like day (n+1) would be 800(.45)^n

..

when is 800(.45)^n = 1

.45^n = 1/800 = .00125

take log of both sides

log(.45^n) = log .00125

n log .45 = log .00125

n = log .00125/log .45 = 8.3

checking:

day 9 = 800(.45)^8 = 1.35

day 10 = 800(.45)^9 = .61 ----> receive no income

so he receives income for 9 days

so we want the sum of the geometric series of 9 terms

with a = 800 and r = .45

sum(9) = 800(1 - .45^9)/(1 - .45)

= 1453.44

- Math -
**Lizzie**, Monday, May 7, 2012 at 9:44pm
I understand it now! Thank you so much!

- Math -
**Anonymous**, Sunday, January 19, 2014 at 5:30pm
i still don't get it

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