Probably easy question, but I dont know how... please help

[Cole1]

Can anyone please help me set up a formula to get the answer to this question?

If someone works for .01 the first day, .02 the next, .04 the next, .08 the next, etc. How much money will he have earned after 20 days? 52 days? N days?

Thank you in advance for any help!!

 

[soroban]

Re: Probably easy question, but I dont know how... please he

Hello, Cole1!

Can anyone please help me set up a formula to get the answer to this question?

If someone works for .01 the first day, .02 the next, .04 the next, .08 the next, etc.
how much money will he have earned after 20 days? 52 days? N days?

Change everything to cents.
The daily salary will be: 1, 2, 4, 8, 16, . . .

This is a geomtric sequence with first term $\displaystyle a\,=\,1$ and common ratio $\displaystyle r\,=\,2$

The sum of the first $\displaystyle n$ terms is: $\displaystyle \,S_n\;=\;a\cdot\frac{r^n\,-\,1}{r\,-\,1}$

Our formula is: \(\displaystyle \,S_n\;=\;1\cdot\frac{2^n\,-\.1}{2\,-\,1}\;=\;2^n\,-\,1\)

By the 20th day, he has received: $\displaystyle \,S_{20}\;=\;2^{20}\,-\,1\:=\:1,048,575$¢ $\displaystyle \,=\,\$10,485.75$

By the 52nd day, he has received: $\displaystyle \, 2^{52}\,-\,1\:\approx\;\$45,036,000,000,000$ . . . over forty-five trillion dollars!

 

[Cole1]

Thank you so much!!! I hate to admit it but I don't understand. I see the answer is correct. Where did you get the 2 in the equation 2^n - 1?

Thanks again!!

 

[Gene]

2 is the ratio of any two days wage. If it is w on one day, the next day it is 2w.

 

[Denis]

Example using 5 days:

day or n  :   1    2    3    4     5....
day's pay :   1    2    4    8    16....
pay so far:   1    3    7   15    31....

On day 5, he earns 16 cents, and has earned 1+2+4+8+16 = 31 to that point.
2^5 = 32 ; 32 - 1 = 31
so: 2^n - 1 (as per Soroban)

 

[mathademically_challenged]

this is probably easy but i'm clueless :!:

a bag contains 4 red and 6 blue marbles. a marble is drawn and is not replaced. then a second marble is drawn
a.identify the first and second events
b.find P(second event | first event
Problems

1.both marbles are red 2.both marbles are blue

3.the first marble is blue and the second is red

4.the first marble is red and the second is blue
i dont even know where to start!!!!!! ~~Sarah~~

 

[jolly]

Why did you post your problem here? Start a new thread for new problems.