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)