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 had a bank account. He was diligent in saving money and his account balance grew over time. To track his progress, he decided to graph his account balance against time.
In the beginning, James did not have much money, so his account balance started at zero. As time went on, James started earning income and deposited it into his account. With each deposit, his account balance increased steadily. The function represented by the graph was increasing during this period.
James was proud of his efforts and continued to save more money. He got a promotion at work and received a significant bonus. As a result, he made larger deposits into his account, causing his balance to increase at a faster rate. The function represented by the graph was still increasing, but at a steeper slope.
However, life is full of ups and downs, and James encountered some unexpected expenses. He needed to pay for car repairs and medical bills, which required him to withdraw money from his account. As a result, his account balance started to decrease. The function represented by the graph was now decreasing.
James was determined to bounce back from these setbacks. He cut down on unnecessary expenses and looked for additional sources of income. He took on extra freelance work and started saving more aggressively. Over time, his account balance began to increase once again. The function represented by the graph was now increasing once more.
James noticed that the function represented by the graph was always increasing during periods when he was saving and depositing money into his account. On the other hand, it was decreasing when he had to withdraw money or faced unexpected expenses. This realization helped him understand the relationship between his actions and the financial state of his account.
With each passing year, James continued to save and invest wisely, steadily increasing his account balance. The graph served as a constant reminder of his dedication and financial discipline. James was proud of how far he had come and remained committed to his financial goals.