Final answer:
The specific week when the money in Ken's account was increasing at an average rate of $12 per day cannot be determined based on the given information.
Step-by-step explanation:
To determine the week when the money in Ken's account was increasing at an average rate of $12 per day, we need the change in the account balance for each week. Unfortunately, the information provided does not include this information. Without the change in balance, it is not possible to identify the specific week. Therefore, the answer cannot be determined based on the given information.