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 savings account at a bank. James was very diligent and decided to keep track of his account balance over time using a graph. The x-axis of the graph represented time in months, while the y-axis represented his account balance in dollars.
As the months passed, James made consistent monthly deposits into his savings account. These deposits were represented by the upward slope of the graph. Whenever James received his paycheck, he would set aside a certain amount to save for the future. This led to an increase in his account balance over time. The function represented by the graph was increasing during this period.
However, as life has its ups and downs, James occasionally had unexpected expenses. These expenses were represented by the downward slope of the graph. For example, there was a month when James had to pay for car repairs, and another month when he went on a vacation. These expenses caused a temporary decrease in his account balance. The function represented by the graph was decreasing during these periods.
Despite the occasional ups and downs, James remained committed to saving money and managing his expenses wisely. He understood that the long-term trend was still upwards, indicating his growing savings. The graph of his account balance served as a reminder of his financial progress and motivated him to continue making deposits and controlling his spending.
In conclusion, the function represented by the graph was increasing when James made consistent monthly deposits and decreasing when he faced unexpected expenses. Through his dedication and financial discipline, James was able to build a stable and growing savings account over time.