Unformatted text preview: cal hot air balloon expands as the air inside the balloon is heated. The radius of the
balloon, in feet, is modeled by a twicedifferentiable function r of time t, where t is measured in minutes. For
0 < t < 12, the graph of r is concave down. The table above gives selected values of the rate of change, r ¢(t ) ,
of the radius of the balloon over the time interval 0 £ t £ 12. The radius of the balloon is 30 feet when t = 5.
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(Note: The volume of a sphere of radius r is given by V = p r 3 . )
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(a) Estimate the radius of the balloon when t = 5.4 using the tangent line approximation at t = 5. Is your
estimate greater than or less than the true value? Give a reason for your answer.
(b) Find the rate of change of the volume of the balloon with respect to time when t = 5. Indicate units of
measure.
(c) Use a right Riemann sum with the five subintervals indicated by the data in the table to approximate
12 Ú0 r ¢(t ) dt. Using correct units, explain the meaning of 12 Ú0 (d) Is your...
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 Spring '09
 Phalange
 Derivative, Hot air balloon, The College Board

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