Linear versus exponential IRL 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 appears in the exponent. It can be represented by the equation y = a(b^x), where a is a constant, b is the base, and x is the exponent.

Front

Identify the type of function: "A gym’s customers must pay $50 for a membership, plus $3 for each time they use the gym."

Back

Linear

Front

Identify the type of function: "A library has 8000 books, and is adding 500 more books each year."

Back

Linear

Front

Identify the type of function: "A science experiment involves periodically measuring the number of mold cells present on a piece of bread. At the start of the experiment, there are 50 mold cells. Each time a periodic observation is made, the number of mold cells triples."

Back

Exponential

Front

Write an equation for: "A gym’s customers must pay $50 for a membership, plus $3 for each time they use the gym."

Back

y = 3x + 50

Front

Write an equation for: "At the start of a carnival, you have 50 ride tickets. Each time you ride the roller coaster, you have to pay 6 tickets."

Back

y = 50 - 6x

Front

What does the slope represent in a linear function?

Back

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

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base of the exponent in the function, indicating how much the quantity increases or decreases with each unit increase in x.