Semester Exam Review Part 5

Front

What is the formula to calculate the future population given an initial population and a constant growth rate?

Back

The future population can be calculated using the formula: \( P = P_0 (1 + r)^t \) where \( P_0 \) is the initial population, \( r \) is the growth rate (as a decimal), and \( t \) is the number of years.

Front

What is the Vertical Line Test and how is it used to determine if a relation is a function?

Back

The Vertical Line Test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function. A function must have only one output for each input.

Front

How do you solve a system of linear equations using substitution?

Back

To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the significance of the growth rate in population studies?

Back

The growth rate indicates how quickly a population is increasing or decreasing, which is crucial for planning resources and services.

Front

How do you convert a percentage increase to a decimal for calculations?

Back

To convert a percentage increase to a decimal, divide the percentage by 100. For example, an 8% increase becomes 0.08.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is \( Ax + By = C \), where A, B, and C are constants.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be graphically represented as a straight line, which means it has a constant rate of change.

Front

How do you find the slope of a line given two points?

Back

The slope \( m \) can be calculated using the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \) where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points.

Front

What is the difference between a dependent and independent variable?

Back

An independent variable is the variable that is changed or controlled in an experiment, while a dependent variable is the variable being tested and measured.