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PLEASE HELP ALGEBRA 2!!!
Raul deposits $400 in a savings account over the course of a year. He deposits money into the account throughout the next year until his balance is tripled. The next year he does the same and deposits money into the account until his previous year’s balance is tripled. Assume that this trend continues and his account does not earn interest. Consider his initial balance to be year one. What explicit formula can be used to determine the balance of his savings account at the end of n years?

Respuesta :

1. Let [tex]y_n [/tex] represent the balance after year n

2. So for example [tex]y_1[/tex] represents the balance after year 1, [tex]y_2[/tex] the balance after year 2 and so on

3. so :

[tex]y_1=400[/tex]

[tex]y_2=400*3[/tex]

[tex]y_3=400*3*3[/tex]

[tex]y_4=400*3*3*3[/tex]

so notice that the diference of year n and the number of 3's we multiply is 1

so [tex]y_n=400*3^{n-1}[/tex] is the formula which gives the balance after n years