The relationship between Jame’s account balance and time is modeled by the graph below:
Write a story that models the situation represented by the graph.
When is the function represented by the graph increasing? How does this relate to your story?
When is the function represented by the graph decreasing? How does this relate to your story?
Once upon a time, there was a young man named James who decided to open a savings account at a local bank. He started with an initial balance of $100 and began tracking his account balance over time.
As time went on, James made regular deposits into his account, increasing his balance. The more money he deposited, the higher his account balance climbed. This upward trend continued for a period of time, representing the increasing function of the graph. It showed that James's account balance was growing steadily over time.
However, life is unpredictable, and James encountered some unexpected expenses. There were times when he had to withdraw money from his savings account, decreasing his balance. These instances of withdrawal were evident in the decreasing function of the graph. It demonstrated that James had to dip into his savings at certain points in time, causing his account balance to decrease momentarily.
Despite the occasional decrease, James always strived to maintain a positive overall growth in his savings. He recognized the importance of saving money and worked hard to increase his account balance whenever possible.