Answer:
. In conclusion, to identify the best function to represent the data for the growth of Eric's home value, it is necessary to analyze the actual data points and plot them on a graph. This will enable us to visually assess the pattern and determine if it aligns with a linear, quadratic, or exponential function.
Explanation:
To determine the best function that represents the data for the growth of Eric's home value over the past four years, let's first understand the characteristics of linear, quadratic, and exponential functions. 1. Linear Function: A linear function has a constant rate of change and forms a straight line when graphed. It is represented by the equation y = mx + b, where m is the slope and b is the y-intercept. Linear functions describe situations where the change is constant over time. 2. Quadratic Function: A quadratic function has a squared term and forms a parabola when graphed. It is represented by the equation y = ax^2 + bx + c, where a, b, and c are constants. Quadratic functions describe situations where the rate of change is not constant and can accelerate or decelerate. 3. Exponential Function: An exponential function has a constant ratio between consecutive terms and forms a curve when graphed. It is represented by the equation y = ab^x, where a is the initial value, b is the base, and x is the exponent. Exponential functions describe situations where the growth or decay rate is proportional to the current value. Now, let's analyze the given data to determine the best function to represent the growth of Eric's home value: - Linear: If the data points form a straight line when plotted on a graph, a linear function would be a good fit. In a linear function, the rate of change is constant. If the data points show a consistent increase or decrease over time, a linear function could be appropriate. - Quadratic: If the data points form a curve (like a parabola) when plotted on a graph, a quadratic function might be suitable. Quadratic functions represent situations where the rate of change is not constant. If the data points show an accelerating or decelerating growth pattern, a quadratic function could be considered. - Exponential: If the data points show a consistent growth or decay rate, an exponential function could be a good choice. Exponential functions represent situations where the growth or decay rate is proportional to the current value. If the data points exhibit a consistent doubling or halving pattern, an exponential function might be appropriate. Based on the information provided, it is difficult to determine the best function without the actual data or a clear description of the growth pattern. To make a more accurate determination, it would be helpful to see the actual data points and plot them on a graph. This would allow us to visually analyze the pattern and make a more informed decision about the type of function that best represents the data. In conclusion, to identify the best function to represent the data for the growth of Eric's home value, it is necessary to analyze the actual data points and plot them on a graph. This will enable us to visually assess the pattern and determine if it aligns with a linear, quadratic, or exponential function.