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 start saving money for his dream vacation. He opened a special savings account and made regular deposits into it over time. The relationship between James' account balance and time was beautifully represented by a graph.
In James' story, the function represented by the graph is increasing when the line on the graph is going up. This means that as time passes, his account balance is growing. It implies that James is diligently adding money to his savings account at a consistent rate. Perhaps he is following a strict budget, and every month, he sets aside a fixed amount of his income to save for his vacation. This positive trend in the graph shows James' commitment and progress towards his monetary goal.
On the other hand, the function represented by the graph is decreasing when the line on the graph is going down. This means that James' account balance is decreasing over time. This scenario could be attributed to certain circumstances beyond James' control. For example, he may have faced an unexpected expenditure that impacted his savings, such as a car repair or medical bill. Alternatively, James might have dipped into his savings to make a special purchase or to cover some additional expenses. The decreasing trend in the graph suggests that James' account balance is getting smaller, calling for a need to reassess his spending habits or make adjustments to his financial plans.
Overall, James' journey towards saving for his dream vacation is beautifully represented by the graph, showing the ups and downs, the progress made over time, and the challenges he may face along the way.