Exponential word problem I'm having trouble with

Apr 2013
4
0
Columbia, Maryland
1.) Jerry's daughter Marty has asked him to consider a change in her allowance. She has proposed that he pay her 2 cents this week and that he double the amount each week. It sounds good for this week but Jerry is suspicious! How much would Jerry pay in week 5? Week 15? Week 25? Week 50? Should Jerry accept this proposal?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
What difficulty are you having? Do you understand that this is just arithmetic? You know how to multiply by 2, dont you? The first week would be 2 cents, the second week, 4 cents, the third week 8 cents, the fourth week 16 cents, the fifth week 32 cents.... You can continue just multiplying by two but the problem will be simpler if you recognise those numbers as "powers of 2": \(\displaystyle 2= 2^1\), \(\displaystyle 4= 2^2\), \(\displaystyle 8= 2^3\), \(\displaystyle 16= 2^4\), \(\displaystyle 32= 2^5\).... Get the idea?
 
Apr 2013
4
0
Columbia, Maryland
yeah, just a little rusty at it
 
Nov 2007
985
175
Trumbull Ct
This is a geometric progression problem. Formula is
n^th term = a*r^(n-1) where a is the first term r is ratio between each term and n is the number of term

For 57^th week 2*2^56 =2^57 = 1.44 *10^17 or 1.44* 10 ^15 dollars (quadtrillion)