# rates of change word problem

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• December 8th 2009, 06:13 PM
extraordinarymachine
rates of change word problem
I need help setting up this word problem, i know i need to use limits

The distance an airplane has flown at t hours is given by
S(t) = 600t + $30t^2 - 4t^3$, where S is the distance in kilometers and 0 $x\leq t\leq 5$. Estimate the instantaneous rate of change in distance at exactly 2 h.
• December 8th 2009, 08:58 PM
am1
S(t) = 600t + 30t^2 - 4t^3 (distance of the airplane in km with respect to time-t )
s'(t) = 600 + 60t - 12t^2 (instantaneous rate with respect to "t" in hours)
s'(2) = 768 km/h