Question

Diane deposited $1,000 into a checking account. Each week she withdraws $25 from the account. She makes no other deposits or withdrawals. The amount of money remaining in the bank account is a function of the number of weeks that have passed. What is the domain that relates to the function that represents this situation?

a) All real numbers between 0 and 40
b) All real numbers between 0 and 1,000
c) All integers from 0 to 40
d) All integers divisible by 25 from 0 to 1,000

Answer 1

The domain of the function where Diane deposited $1,000 and withdraws $25 each week is all integers from 0 to 40, representing the number of weeks she can make withdrawals before the account balance reaches zero.

Step-by-step explanation:

The domain that relates to the function representing the situation where Diane deposited $1,000 into a checking account and withdraws $25 each week is the set of values that the independent variable (weeks in this case) can take. Since Diane can only withdraw $25 for as many weeks as she has money in her account, and given that she makes no other deposits or withdrawals, this function will have a limited domain. For each week that passes, $25 is subtracted from the initial deposit of $1,000. After 40 weeks, she would have withdrawn a total of $1,000 ($25 * 40 = $1,000). This implies that the domain of the function is the set of all weeks from 0 to 40, where she still has money in her account, including the start (week 0 with $1,000) and the end (week 40 with $0 left). It's also important to note that she can't withdraw a fraction of a week - only whole weeks - making the domain consist of whole numbers (integers). Therefore, the correct answer is c) All integers from 0 to 40.