Estimate the radius of the ballon

Reference no: EM131014931

The volume of a spherical hot air ballon expands as the air inside the ballon is heated. The radius of the ballon, in feet, is modeled by a twice-differentiable function r(t), where t is measured in minutes. The table below gives selected values of the rate of change, r'(t) of the radius of the ballon over the time interval 0 ≤ t ≤ 12. The radius of the ballon is 30 feet when t = 5. Note the volume of the sphere of radius r is given by V = (4/3) π r³. Estimate the radius of the ballon when t = 4.8. Find the rate of change of the volume of the ballon with respect to time when t = 5. Show that there must be some time when the rate of change of the radius of the ballon is 3 feet per minute. Estimate the rate of change of r'(t) at t = 9.

T (minutes)	0	2	5	7	11	12
r' (t) (feet per minute)	5.7	4.0	2.0	1.2	0.6	0.5

Reference no: EM131014931

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