1. A spherical balloon is being inflated. The radius, r, of the balloon is 0 cm initially, and is increasing at a constant rate of 2 cm per second. a) State the equation for the volume, V, of the balloon with respect to the radius, r, and the equation for the radius of the balloon with respect to t, the time elapsed in seconds. i.e. find V(r) and r(t) b) Determine an algebraic representation of (V •r)(t). Describe what this formula means in words. c) Determine the volume of the balloon at 5 sec d) Suppose the balloon will burst when its volume is 10 000 cm³. How long will it take for the balloon to burst?

1. A spherical balloon is being inflated. The radius, r, of the balloon is 0 cm initially, and is increasing at a constant rate of 2 cm per second. a) State the equation for the volume, V, of the balloon with respect to the radius, r, and the equation for the radius of the balloon with respect to t, the time elapsed in seconds. i.e. find V(r) and r(t) b) Determine an algebraic representation of (V •r)(t). Describe what this formula means in words. c) Determine the volume of the balloon at 5 sec d) Suppose the balloon will burst when its volume is 10 000 cm³. How long will it take for the balloon to burst?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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