Algebra 1: Linear vs. Exponential Functions

Front

What is the main difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, characterized by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How can you identify a linear situation in real life?

Back

A linear situation can be identified by a constant change over equal intervals, such as a fixed amount of money being added or deducted regularly.

Front

How can you identify an exponential situation in real life?

Back

An exponential situation can be identified by a percentage increase or decrease over time, such as interest earned on a savings account.

Front

What does it mean for a function to be linear?

Back

It means that the relationship between the variables can be represented by a straight line, indicating a constant rate of change.

Front

What does it mean for a function to be exponential?

Back

It means that the relationship between the variables grows or decays at a rate proportional to its current value, resulting in a curve that increases or decreases rapidly.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

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

Back

The base in an exponential function determines the growth or decay rate; if the base is greater than 1, the function represents growth, and if it is between 0 and 1, it represents decay.

Front

What is the slope of a linear function?

Back

The slope of a linear function represents the rate of change of the function, indicating how much y changes for a unit change in x.