Practice 40: Choose a Regression Model

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What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

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What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to rapid increases over time. For example, if a population triples each year, it is experiencing exponential growth.

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What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to rapid decreases over time. For example, if a substance's quantity halves every hour, it is experiencing exponential decay.

Front

How can you identify a linear function?

Back

A linear function can be identified by its constant rate of change, represented by a straight line on a graph. The general form is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage. This leads to very different growth patterns over time.

Front

What is a scatter plot?

Back

A scatter plot is a graphical representation of two variables, showing the relationship between them. Each point represents an observation, and the pattern of points can indicate the type of association (linear, exponential, etc.).

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What does it mean for a scatter plot to have a negative association?

Back

A negative association in a scatter plot means that as one variable increases, the other variable tends to decrease. This is represented by a downward trend in the plotted points.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax^2 + bx + c, where 'a', 'b', and 'c' are constants. Its graph is a parabola.

Front

What is the significance of the base in an exponential function?

Back

The base in an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you determine if a function is linear, exponential, or neither?

Back

To determine the type of function, analyze the rate of change: if it is constant, it is linear; if it increases or decreases by a percentage, it is exponential; if neither condition is met, it is neither.