The radius of the balloon in feet is modeled by a

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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 twice-differentiable 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. 4 (Note: The volume of a sphere of radius r is given by V = p r 3 . ) 3 (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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