Linear vs Exponential Tables

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change and can be expressed in the form 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 in which an independent variable is in the exponent. It can be expressed in the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference between consecutive y-values for equal increments in x-values.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will have a constant ratio between consecutive y-values for equal increments in x-values.

Front

What is the common difference in a linear sequence?

Back

The common difference is the amount added to each term to get the next term in a linear sequence.

Front

What is the common ratio in an exponential sequence?

Back

The common ratio is the factor by which each term is multiplied to get the next term in an exponential sequence.

Front

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

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time.

Front

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.

Front

Given the sequence 3, 6, 12, 24, what type of function does it represent?

Back

Exponential Growth, as each term is multiplied by 2 to get the next term.

Front

Given the sequence 10, 8, 6, 4, what type of function does it represent?

Back

Linear, as each term decreases by 2 to get the next term.