Understanding Fuel Volume and Depth Functions

The video tutorial explains how the volume of fuel in a storage tank is related to the depth of the fuel, which in turn depends on time. It introduces the formulas for volume as a function of depth and depth as a function of time. The tutorial demonstrates how to use function composition to express volume as a function of time and simplifies the resulting expression. Finally, it calculates the volume of fuel in the tank after two hours, providing a practical example of the concepts discussed.

What is the formula for the volume of fuel in the tank as a function of depth?

• V(d) = 4 * (3d^2 + 5)^3

• V(d) = 3 * (4d^2 + 5)^3

• V(d) = 4 * (3d^2 + 5)^2

• V(d) = 3 * (4d^2 + 5)^2

How does the depth of fuel change over time according to the given formula?

• d(t) = sqrt(3) * (sqrt(t) - 5)

• d(t) = sqrt(3) / (sqrt(t) - 5)

• d(t) = 1 / (sqrt(3) * sqrt(t) - 5)

• d(t) = 1 / (sqrt(3) * sqrt(t) + 5)

What is the first step in composing the volume function as a function of time?

• Replace t with d in the volume formula

• Replace d with t in the depth formula

• Replace d with the depth function in the volume formula

• Replace t with the volume function in the depth formula

What is the simplified expression for the volume as a function of time?

• V(t) = 4t^3

• V(t) = 3t^3

• V(t) = 4t^2

• V(t) = 3t^2

How many cubic meters of fuel are in the tank after 2 hours?

• 16 cubic meters

• 24 cubic meters

• 40 cubic meters

• 32 cubic meters