Linear Vs Exponential

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

Front

Define a linear function.

Back

A linear function is a function that graphs to a straight line, represented 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

What does the term 'slope' refer to in a linear function?

Back

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

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, represented as the point (0, b) in the equation y = mx + b.

Front

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

Back

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

Front

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

Back

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

Front

What is the starting point of an exponential function?

Back

The starting point of an exponential function is the value of y when x is 0, often represented as 'a' in the equation y = ab^x.

Front

Give an example of a real-world situation that represents linear growth.

Back

Earning a fixed amount of money each week, such as $5 per week.

Front

Give an example of a real-world situation that represents exponential growth.

Back

The growth of bacteria, where the population doubles at regular intervals.