Exploring Absolute, Relative, and Percent Change

What is the formula for calculating the true absolute change in a function?

• f(a + dx) / f(a)

• f(a) * dx

• f(a) - f(a + dx)

• f(a + dx) - f(a)

How do you convert relative change into percent change?

• Subtract 100

• Divide by 100

• Multiply by 100

• Add 100

What is the estimated absolute change in the perimeter of a bicycle tire when its radius changes from 12 inches to 13 inches?

• 2 inches

• 2π inches

• 24π inches

• 0.08 inches

What is the relative change in the perimeter of the bicycle tire when the radius changes from 12 inches to 13 inches?

• 0.08

• 0.12

• 0.04

• 0.10

What is the formula for the surface area of a sphere?

• 4πr

• 2πr²

• 4πr²

• πr²

How does a 0.1 mile change in the Earth's radius affect its surface area?

• It increases by approximately 9,995 square miles

• It decreases by approximately 9,995 square miles

• It increases by approximately 99,950 square miles

• It decreases by approximately 99,950 square miles

To keep the surface area within 1% of its true value, what should be the maximum error in measuring the radius of a sphere?

• 1%

• 0.5%

• 2%

• 0.1%

What is the formula discovered by Jean Poiseuille for fluid flow through a tube?

• V = k r²

• V = k r³

• V = k r⁴

• V = k r

How does a 10% increase in the radius of a tube affect the volume of fluid flow according to Poiseuille's formula?

• 40% increase

• 30% increase

• 20% increase

• 10% increase

What is the relative change in volume if the radius of a tube is increased by 10%?

• 40%

• 30%

• 20%

• 10%