Answer :
Final answer:
The instantaneous rate of change of the volume after 10 minutes is -7500 cubic units per minute.
Explanation:
The question is asking for the instantaneous rate of change of a volume function. The rate of change is calculated by finding the derivative of the function, and the instantaneous rate of change at a certain point can be found by substituting that point into the derivative function.
The derivative of V(t) = 3000(1 - 0.5t)^2 is V'(t) = -3000*(1 - 0.5t)*0.5. To find the rate of change after 10 minutes, we let t=10 in V'(t), which gives -3000*(1 - 0.5*10)*0.5 = -7500 cubic units per minute. So, the volume is decreasing at a rate of 7500 cubic units per minute after 10 minutes.
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