Understanding Ice Sheet Melting and Linear Functions

The video tutorial explains the melting of an ice sheet near the Arctic Circle, which decreases in thickness at a constant rate. It introduces the function S(t) to represent the ice thickness over time, calculates the rate of change, and explains how to express this as a linear function. The tutorial also covers the concepts of slope and intercept in the context of the function, encouraging viewers to graph the function for better understanding.

What is the initial thickness of the ice sheet near the Arctic Circle?

• 3 meters

• 0.75 meters

• 2 meters

• 1.25 meters

After how many weeks does the ice sheet's thickness reduce to 1.25 meters?

• 3 weeks

• 1 week

• 2 weeks

• 4 weeks

What is the change in thickness of the ice sheet over three weeks?

• 0.5 meters

• 0.75 meters

• 1 meter

• 1.25 meters

What is the rate of change of the ice sheet's thickness per week?

• -1 meter per week

• -0.25 meters per week

• -0.5 meters per week

• -0.75 meters per week

Which form is used to express a linear function?

• y = log(x)

• y = a/x

• y = ax^2 + bx + c

• y = mx + b

In the linear function S(t) = -0.25t + 2, what does the number 2 represent?

• The time in weeks

• The initial thickness

• The final thickness

• The rate of change

What does the slope of the linear function indicate in this context?

• The final thickness of the ice

• The rate at which the ice melts

• The total time taken for the ice to melt

• The initial thickness of the ice

How does the thickness of the ice sheet change every week according to the function?

• Decreases by 0.5 meters

• Increases by 0.5 meters

• Decreases by 0.25 meters

• Increases by 0.25 meters

What is the significance of the negative sign in the rate of change?

• It indicates the ice is getting thicker

• It shows the ice is melting

• It means the ice is freezing

• It suggests the ice is stable

What would be the thickness of the ice sheet after 4 weeks?

• 0.5 meters

• 1 meter

• 0.25 meters

• 0.75 meters