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Let 
be the amount of money he has in the account at the end of the 
th month.
So at the end of the first month (assuming he doesn't make a withdrawal then) he would have
.
Halfway through the next month, he withdraws 1/3 of the account. The account doesn't earn interest, so only his withdrawals affect the amount of money in the bank. So at the end of the second month, he would have
At the end of the third,
And so on. So the recursive rule is
starting with.
So at the end of the first month (assuming he doesn't make a withdrawal then) he would have
Halfway through the next month, he withdraws 1/3 of the account. The account doesn't earn interest, so only his withdrawals affect the amount of money in the bank. So at the end of the second month, he would have
At the end of the third,
And so on. So the recursive rule is
starting with
Answer:
Step-by-step explanation:
Let d be the number of days.
We have been that each day Katie finds 12 more seashells on beach, so after collecting shells for d days Katie will have 12d shells.
We are also told that Katie already has 34 seashells in her collection, so total number of shells in Katie collection after d days will be:
As Katie wants to collect over 100 seashells, so the total number of shells collected in d days will be greater than 100. We can represent this information in an inequality as:
Therefore, the inequality can be used to find the number of days, d, it will take Katie to collect over 100 seashells.