SOLUTION: You plan to save 1 cent the first day of the month, 2 cents the second day, 4 cents the third day, and to continue this pattern of saving on the preceding day for every day in a mo

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Question 50105This question is from textbook Applied College Algebra
: You plan to save 1 cent the first day of the month, 2 cents the second day, 4 cents the third day, and to continue this pattern of saving on the preceding day for every day in a month that has 30 days.
a. How much money, in dollars, willyou need to save on the 30th day?
b. How much money, in dollars, will you have saved after 30 days? (Suggestion: Note that after 2 days, you have saved 2^2 - 1 = 3 cents; after 3 days, you have saved 2^3 - 1 = 7 cents; and after 4 days, you have saved 2^4 - 1 = 15 cents.)This question is from textbook Applied College Algebra

Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
You plan to save 1 cent the first day of the month, 2 cents the second day, 4 cents the third day, and to continue this pattern of saving on the preceding day for every day in a month that has 30 days.
a. How much money, in dollars, willyou need to save on the 30th day?
DAY 1...........=1=2^0
DAY 2...........=2=2^1
DAY 3...........=4=2^2
DAY 4...........=8=2^3
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DAY 30............=2^(30-1)=2^29=536870912 C= 5368709.12 $

b. How much money, in dollars, will you have saved after 30 days? (Suggestion: Note that after 2 days, you have saved 2^2 - 1 = 3 cents; after 3 days, you have saved 2^3 - 1 = 7 cents; and after 4 days, you have saved 2^4 - 1 = 15 cents.)
CORRECT ..THIS IS A GEOMETRIC SEQUENCE WHOSE SUM IS GIVEN BY
Sn=A*(R^N - 1)/(R-1)....WHERE Sn =SUM AFTER N DAYS,A=1 ST DAY DEPOSIT
R=COMMON RATIO OF INVREASE. WE HAVE N=30,A=1,R=2
SO S
S30=2^30 -1 =1073741823 C = 10737418.23 $