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Michelle deposits money into the bank every month. On the first month, she deposits $4. Each month after, Michelle deposits 3 times as much as she did the month before. Write an equation to model her monthly deposit,

User Gowtham S
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Answer:

This formula gives us the amount that Michelle deposits in any given month, based on the month number. For example, the deposits for the first 5 months would be:

D_1 = 4

D_2 = 3D_1 = 12

D_3 = 3D_2 = 36

D_4 = 3D_3 = 108

D_5 = 3D_4 = 324

And so on.

Explanation:

Let's start by defining some variables to represent the problem:

Let D_n be the amount Michelle deposits in the nth month.

Let n be the month number, with n=1 representing the first month.

According to the problem, Michelle deposits $4 in the first month (n=1). In the following months (n>1), she deposits 3 times as much as she did the month before. Therefore, we can write the following recursive formula for the monthly deposits:

D_1 = 4 (first month deposit)

D_n = 3*D_(n-1) (for n>1, deposit is 3 times previous month's deposit)

Alternatively, we can write an explicit formula for the nth month's deposit by using the recursive formula and simplifying it using the properties of geometric sequences:

D_n = 4*3^(n-1) (for n>=1)

This formula gives us the amount that Michelle deposits in any given month, based on the month number. For example, the deposits for the first 5 months would be:

D_1 = 4

D_2 = 3D_1 = 12

D_3 = 3D_2 = 36

D_4 = 3D_3 = 108

D_5 = 3D_4 = 324

And so on.

(Reference to Chatgpts work)

User Cpuguru
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