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what is the formula for finding how much money a babysitter would make if her rate was doubled for every hour she worked?

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4 Answers

Geometric Progression Formula is;
Sn = a1 (rn-1) / (r - 1) and n ≠ 1
where
Sn = total at n
a1 = initial value = 3 dollars
r is the common ratio = 2 (rate doubles every hour)
n = hour number (hour 5)
Sn = 3 (2n-1) / (2 - 1) = 3 (2n) - 3
S5 = 3 (25) - 3 = $ 93
Rate  = 3, 6, 12, 24,48 dollars/hour (1st to 5th hourly rate)
Total = 3 ,9, 21, 45, 93 dollars total (1st to 5th pay totals)
Hey Samuel -- you may "spell out" a brief sequence to verify ...
3 ... 6 ... 12 .... 24 .... 48 ... 96 ==> sitter makes 93 of those dollars (subtract initial 3)
   10am, 11am, noon, 1pm, 2pm ... Regards, sir :)
If something is doubled every hour (or, in general, every time interval t) then
 
S=S02t; Here S0 is the initial quantity one has, t is time.
 
Example: after 1 hour S=S0*21=2S0.
After 2 hours S=S0*22=4S0. And so on and so forth.
 
Here you have t=5, S0=3. Then S=3*25=3*32=96
These is a geometric sequence with ratio = 2. Let C(t) represent the money you have after t hours of babysitting.
C(0) = 3
C(n) = 3*2^(n)
From 9 am to 2 pm, there are 5 hours. So, n = 5, and
C(5) = 3*2^5 = 96 dolloars