You have 3 dollars. Your mom says that she will double your money for every hour that you babysit your sister. your mom goes shopping at the mall from 9:00 AM to 2:00 PM. Write an equation using function notation that models this situation.

## 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;

**S**and n ≠ 1

_{n}= a_{1}(r^{n}-1) / (r - 1)where

_{Sn}= total at n

a

_{1}= initial value = 3 dollarsr is the common ratio = 2 (rate doubles every hour)

n = hour number (hour 5)

S

_{n}= 3 (2^{n}-1) / (2 - 1)**= 3 (2**^{n}) - 3S

_{5}= 3 (2^{5}) - 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=S

_{0}2^{t}; Here S_{0}is the initial quantity one has, t is time.Example: after 1 hour S=S0*2

^{1}=2S_{0}.After 2 hours S=S

_{0}*2^{2}=4S_{0}. And so on and so forth.Here you have t=5, S

_{0}=3. Then S=3*2^{5}=3*32=96These 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