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WILL MARK BRAINLIEST!!!! NEED HELP FAST!!!
Lou opens a bank account. The deal he makes with his mother is that if he doubles the amount that was in the account at the beginning of each month by the end of the month, she will add an additional $5 to the account at the end of the month.

a. Let A(n) represent the amount in the account at the beginning of the nth month. Assume that he does, in fact, double the amount every month. Write a recursive formula for the amount of money in his account at the beginning of the (n+1)th month.

b. What is the least amount he could start with in order to have $300 by the beginning of the third month?

Respuesta :

Ziham
I thinks it’s a so yeah I hoped this helped
charlief22

Greetings!

a) As you stated, A(n +1) , this means that as A(n) is a money in the nth month:

2 x A(n) would give you the double money in the bank, and simply add a five on the end and simplify:

2A(n) + 5 = A(n+1)


b) A(3) = 2 x A(n) + 5

   A(3) = 2 x ( 2 x A(1) +5) +5

   Now just simplify this down

A(3) = 4 x A(1) + 15

The least amount needs to equal or be higher than $300, so:

300 ≤ 4 x A(1) + 15

300 -15 ≤ 4 x A(1)

285 ≤ 4 x A(1)

285 / 4 ≤ A(1)

Which gives:

71.25 ≤ A(1)

So he needs $71.25 in the first month so he is over $300 after three months.


Hope this helps!