Question

Question 14 A) Madison's credit card balances, f(x), over the span of x months are shown in the table below. x (number of Months) f(x) (credit card Balance 3 $2,771 6 $3,491 9 $4,398 12 $5,540 15 $6,979 Which type of function is the best model for this data? (1 point) Responses Exponential Function Exponential Function cubic Function cubic Function Quadratic Function Quadratic Function Linear Function Linear Function Question 15 A)In which of the following situations is there most likely to be correlation without causation?(1 point) Responses the number of cars in a city and the number of police officers in the city the number of cars in a city and the number of police officers in the city the number of letters in a person's name and the person's shoe size the number of letters in a person's name and the person's shoe size the number of cars manufactured at a car factory and the amount of metal used at the factory the number of cars manufactured at a car factory and the amount of metal used at the factory the number of people who work in an office building and the number of desks in the office building the number of people who work in an office building and the number of desks in the office building

Answer 1

### Question 14 A)
To determine the best model for Madison's credit card balances over time, we need to analyze the given data points:

- At 3 months: $2,771
- At 6 months: $3,491
- At 9 months: $4,398
- At 12 months: $5,540
- At 15 months: $6,979

From this data, we can observe that the balance increases steadily, but the rate of increase seems to accelerate over time, suggesting a nonlinear relationship.

1. **Linear Function**: Would imply a constant rate of increase, which is not the case here.
2. **Quadratic Function**: May fit, but typically suggests a parabolic relationship rather than exponential growth.
3. **Exponential Function**: Seems likely since the values suggest a rapid increase as time (months) progresses.

Given the increasing growth rate, the best choice here would be **Exponential Function**.

### Question 15 A)
We want to identify a situation where there's likely correlation without causation. Correlation means that two variables move in relation to each other, but that doesn’t mean one causes the other.

- **The number of cars in a city and the number of police officers in the city**: Likely correlated due to city size, but it's not accurate to claim that more cars cause more police officers.

- **The number of letters in a person's name and the person's shoe size**: Likely no correlation and no causation as these are unrelated factors.

- **The number of cars manufactured at a car factory and the amount of metal used at the factory**: Directly correlated, as more cars manufactured would generally require more metal.

- **The number of people who work in an office building and the number of desks in the office building**: This is generally correlated due to the need for desks corresponding to the number of workers.

Considering these options, the situation that represents the most likely correlation without causation is:

**The number of cars in a city and the number of police officers in the city.**