Understanding Linear Functions in Painting

The video tutorial explains how to model a painting problem using a linear function. Hiro paints his room at a rate of eight square meters per hour. After three hours, he has 28 square meters left to paint. The function A(t) represents the area left to paint over time. The tutorial guides through constructing the formula A(t) = -8t + 52, verifying it with units, and exploring alternative approaches.

What is the rate at which Hiro paints his room?

• 12 square meters per hour

• 10 square meters per hour

• 8 square meters per hour

• 5 square meters per hour

How much area is left to paint after three hours?

• 36 square meters

• 20 square meters

• 44 square meters

• 28 square meters

If Hiro has 36 square meters left to paint, how many hours has he been painting?

• 4 hours

• 3 hours

• 2 hours

• 1 hour

What is the initial area Hiro had to paint?

• 48 square meters

• 56 square meters

• 44 square meters

• 52 square meters

What is the formula for the area left to paint as a function of time?

• A(t) = -8t - 52

• A(t) = 8t + 52

• A(t) = -8t + 52

• A(t) = 8t - 52

What does the slope of the function A(t) represent?

• The initial area to paint

• The time taken to paint

• The rate of painting

• The total area to be painted

What is the significance of the intercept in the function A(t)?

• It represents the final area left to paint

• It represents the initial area to paint

• It represents the time taken to paint

• It represents the rate of painting

How can you verify the formula for A(t)?

• By altering the time

• By checking the units

• By using a different rate

• By changing the initial area

What alternative method can be used to derive the formula for A(t)?

• Using a quadratic function

• Using a constant function

• Using the given conditions to solve for b

• Using a logarithmic function

Why is the rate of change negative in the function A(t)?

• Because the area to paint increases over time

• Because the area to paint decreases over time

• Because the initial area is negative

• Because the time decreases over time