If the amount of money duplicates each month, find an expression for it

Question

Sarah is saving money, on the first month, she starts with $1.65 and each month after the money duplicates, for example, 1.65 - 3.3 - 6.6 - 13.2 - 26.4 ... Find an expressions that replaces the number of months with X and tells you how much money she has after that amount of months.                                  

The question is pretty much saying, to write an expression that when you replace X with a random amount of months, you will get the amount of money she has.    Every month her money is double the amount she had the month before, like I said, 1.65 then 3.3 then 6.6 Then 13.2

Answer 1

Let x be the random amount of money and n be the number of days passed and x_n be the new amount of money

 

So day 1 you have 1x

Day 2 x₂ = 2x

Day 3 x₃ = 4x

Day 4 x₄ = 8x

 

As you figured out the coefficient keeps doubling on x

 

That will hopefully lead you to 

x_n = 2^n-1x 

 

Day 1, your initial day, 2^n-1 = 2⁰ = 1 so you have your initial money amount.