PLZ HELP PLZ Pam had a certain amount of money in her checking account at the beginning of the year. At the end of each month she deposits enough money to double the amount currently in her account. Pam also has a loan to pay each month, so immediately after her deposit she withdraws $100 from the account.

Given that January is the first month, which explicit formula defines the amount of money in Pam’s account at the end of the nth month, P(n)?

A) P(n) = 2P(n + 1) + 100 n ≥ 2

B) P(n) = 2P(n + 1) − 100 n ≥ 2

C) P(n) = 2P(n − 1) + 100 n ≥ 2

D) P(n) = 2P(n − 1) − 100 n ≥ 2

2)

If Pam had $500 left in her account at the end of April, how much did she have at the end of January?

A) $50

B) $100

C) $150

D) $200

1. Let P(n) be the amount of money Pam had in her account at the end of n-th month. If Pam deposits enough money to double the amount currently in her account and immediately after her deposit she withdraws $100 from the account, then

[tex]P(n+1)=2P(n)-100,\ n\ge 1.[/tex]

You can rewrite this expression as

[tex]P(n)=2P(n-1)-100,\ n\ge 2.[/tex]

Given that January is the first month, April is the fourth month.

If Pam had $500 left in her account at the end of April, then

[tex]500=2P(3)-100,\\ \\2P(3)=600,\\ \\P(3)=300.[/tex]

If Pam had $300 left in her account at the end of March, then

[tex]300=2P(2)-100,\\ \\2P(2)=400,\\ \\P(2)=200.[/tex]

If Pam had $200 left in her account at the end of February, then

[tex]200=2P(1)-100,\\ \\2P(1)=300,\\ \\P(1)=150.[/tex]

This means Pam had $150 at the end of January.