calculate the amount a person would earn over a period of time if his or her salary were a penny the first day, two cents the second day, and so
on doubling each day.
Day Pay
===============
1 0.01000
2 0.02000
3 0.04000
4 0.08000
5 0.16000
Your total pay is 0.310000
MY QUESTION: I am having trouble finding a math equation that will double the pay for each day. I fiqured out how to get the sum and list the days but I just can't find a math formlua that will calculate the pay so that it will double each day; please help.
pay = [$.01 * 2^(day)] - $.01
To calculate the amount a person would earn over a period of time with doubling pay each day, you can use a geometric sequence.
In this case, the initial amount (first day) is given as 0.01. The pay doubles each day, which means on the second day it would be 2 * 0.01 = 0.02, on the third day it would be 2 * 0.02 = 0.04, and so on.
The general formula for a geometric sequence is:
an = a1 * r^(n-1)
Where:
- an is the nth term of the sequence
- a1 is the first term of the sequence
- r is the common ratio between terms
- n is the position of the term in the sequence
In this case, a1 = 0.01 (the first day's pay), and r = 2 (since the pay doubles each day).
To find the total pay over a period of time, you need to calculate the sum of the sequence. The sum of a geometric sequence is given by the formula:
Sn = a1 * (1 - r^n) / (1 - r)
Where:
- Sn is the sum of the first n terms of the sequence
In this case, you want to find the total pay up to a certain day, so you will substitute n with the total number of days you want to calculate.
For example, if you want to calculate the total pay for 5 days, you would substitute n = 5 into the formula:
S5 = 0.01 * (1 - 2^5) / (1 - 2)
S5 = 0.01 * (1 - 32) / (1 - 2)
S5 = 0.01 * (-31) / (-1)
S5 = 0.31
So the total pay over 5 days would be $0.31.
You can use the same formula to calculate the total pay for any number of days by substituting the appropriate value for n.