Linear versus exponential word problems

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It can be 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 in which an independent variable is in the exponent. It can be represented by the equation y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

Write an equation for a linear function that represents a situation where a gym charges a membership fee plus a fee per visit.

Back

y = 3x + 50, where y is the total cost and x is the number of visits.

Front

How do you determine if a word problem represents a linear or exponential function?

Back

Identify if the change is constant (linear) or if it grows by a percentage (exponential). Linear functions have a constant rate of change, while exponential functions have a variable rate of change.

Front

What does it mean for a function to be linear in the context of a library adding books?

Back

It means the library adds a fixed number of books each year, resulting in a straight-line increase in the total number of books.

Front

Write an equation for an exponential function that represents a bank account that triples every month.

Back

y = 10(3^x), where y is the amount in the account after x months.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0, representing the starting point of the function.

Front

In the equation y = 500x + 8000, what do the coefficients represent?

Back

500 represents the number of books added each year, and 8000 represents the initial number of books.

Front

What is the difference between a constant rate of change and a variable rate of change?

Back

A constant rate of change means the quantity increases by the same amount each time (linear), while a variable rate of change means the quantity increases by a percentage (exponential).

Front

Provide an example of a real-world situation that can be modeled by a linear function.

Back

A person earning a fixed salary plus commission on sales.