Jessica is deflating a spherical balloon that had a radius of 8 centimeters. As

Question

Jessica is deflating a spherical balloon that had a radius of 8 centimeters. As she deflates the balloon at a constant rate of -0.5 centimeters per second. (Recall that the volume of a sphere can be related to its varying radius by the formula V = (4/3) pi r^3. Define a function, f, that gives the radius of the balloon (in centimeters) as a function of the number of seconds that have elapsed since Jessica began deflating the balloon, t. Define a function, g, that gives the volume of the balloon (in cubic centimeters) as a function of the radius of the balloon, r (in centimeters). Which of the following expressions are meaningful in this context? (f(g(r)) g(f(t)) Define a function, h, that gives the volume of the balloon (in cubic centimeters) in terms of the number of seconds elapsed since Jessica began deflating the balloon, t. What is the volume of the balloon 2.6 seconds after Jessica began deflating the balloon?

Explanation / Answer

a. dr/dt = 0.5

b. ( d2 v / dt2 ) = 8 r .

c. g(f(t)).

e. 1259.833

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