Comparing Linear and Exponential Functions

Mr. Bean's lesson covers the distinction between linear and exponential functions, focusing on identifying these functions through various scenarios, including word problems, tables, and graphs. The lesson also introduces the concepts of doubling time and half-life, providing examples and equations to illustrate these ideas. Students learn to create function equations and analyze data to determine function types, enhancing their understanding of algebraic concepts.

What distinguishes an exponential function from a linear function graphically?

• An exponential function graph is a straight line that slopes downwards.

• A linear function graph is always a straight line.

• A linear function graph curves upwards rapidly.

• An exponential function curve increases at a constant rate.

What type of growth does a savings account exhibit when it receives a constant deposit every month?

• Exponential growth

• Linear decay

• Exponential decay

• Linear growth

How do you determine if a relationship is exponential growth?

• By dividing by a constant number

• By multiplying by a percentage

• By adding a constant number

• By subtracting a constant number

What indicates a linear relationship in a table of values?

• Values increase by multiplying

• Values decrease by multiplying

• Values increase by a constant amount

• Values decrease by a constant percentage

What does the slope represent in a linear equation?

• Rate of change

• Decay factor

• Initial value

• Exponential base

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

• It represents the slope of the line.

• It represents the initial value of the function.

• It determines the doubling time of the function.

• It indicates the rate of exponential growth.

What is the base number in an exponential decay equation?

• More than 1

• Less than 1

• 1

• 0

In the context of exponential functions, what does a base greater than 1 indicate?

• Linear growth

• Exponential growth

• Exponential decay

• Linear decay

What does doubling time represent in an equation?

• The time it takes for a quantity to reduce by half

• The time it takes for a quantity to double

• The initial amount of the quantity

• The rate of exponential decay

How is the half-life of a substance determined?

• By the time it takes to increase by a constant amount

• By the time it takes to double in amount

• By the time it takes to reduce to its initial amount

• By the time it takes to reduce by half