Linear vs Exponential Functions Quiz

Decide whether the word problem represents a linear or exponential function. A library has 8000 books, and is adding 500 more books each year.

• Linear

• Exponential

• Neither

• Both

Answer explanation

The library starts with 8000 books and adds a constant 500 books each year. This consistent addition indicates a linear function, as the total number of books increases by the same amount annually.

Decide whether the word problem represents a linear or exponential function. A company starts with 2,000 customers and gains 150 new customers each month.

• Linear

• Exponential

• Neither

• Both

Answer explanation

The library starts with 8000 books and adds a constant 500 books each year. This consistent addition indicates a linear function, as the total number of books increases by the same amount annually.

Decide whether the word problem represents a linear or exponential function. A taxi company charges a flat fee of $10, plus $2 for every mile traveled.

• Linear

• Exponential

• Neither

• Both

Answer explanation

The problem describes a fixed membership fee of $50 plus a variable cost of $3 for each gym visit. This results in a total cost that increases linearly with the number of visits, making it a linear function.

Decide whether the word problem represents a linear or exponential function. A population of bacteria starts at 50 and doubles every hour.

• Linear

• Exponential

• Neither

• Both

Answer explanation

The problem describes a situation where the amount of money triples each month, indicating a constant percentage increase. This is characteristic of exponential growth, not linear, which would involve a constant addition.

Decide whether the word problem represents a linear or exponential function. A car's value starts at $20,000 and decreases by half every year.

• Linear

• Exponential

• Neither

• Both

Answer explanation

The problem describes a situation where the amount of money triples each month, indicating a constant percentage increase. This is characteristic of exponential growth, not linear, which would involve a constant addition.

At the start of a carnival, you have 50 ride tickets. Each time you ride the roller coaster, you have to pay 6 tickets. Is this situation linear or exponential?

• Linear

• Exponential

• Neither

• Both

Answer explanation

This situation is linear because each ride costs a fixed number of tickets (6). The total number of tickets decreases by a constant amount with each ride, indicating a linear relationship.

You have 80 game tokens at an arcade. Each time you play a game, it costs 8 tokens. Is this situation linear or exponential?

• Linear

• Exponential

• Neither

• Both

Answer explanation

This situation is linear because each ride costs a fixed number of tickets (6). The total number of tickets decreases by a constant amount with each ride, indicating a linear relationship.

There are 20,000 owls in the wild. Every decade, the number of owls is halved. Is this situation linear or exponential?

• Linear

• Exponential

• Neither

• Both

Answer explanation

The number of owls decreases by half every decade, indicating a consistent percentage decrease rather than a fixed amount. This pattern is characteristic of exponential decay, making the situation exponential.

A population of 10,000 rabbits decreases by half every 5 years. Is this change best described as linear or exponential?

• Linear

• Exponential

• Neither

• Both

Answer explanation

The number of owls decreases by half every decade, indicating a consistent percentage decrease rather than a fixed amount. This pattern is characteristic of exponential decay, making the situation exponential.

Given the table with x-values 1 to 8 and y-values 4, 7, 10, 13, 16, 19, 22, 25, is the function linear or exponential?

• Linear

• Exponential

• Neither

• Both

Answer explanation

The y-values increase by 3 for each increment of 1 in x, indicating a constant rate of change. This consistent difference confirms the function is linear, not exponential.