A water tank is being drained. The function \( V(m) \) gives the volume of water in gallons after m minutes. If \( V(10)=500 \) and \( V(20)=200 \), what is the average rate of change from 10 to 20 minutes?
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7. A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. t (min) | 5 | 10 | 13 | 14.5 | 15 | 20 | 25 | 30 V (gal) | 694 | 444 | 328 | 275 | 250 | 111 | 28 | 0 a. Find the average rate of change in volume from 10 minutes to 15 minutes after the water begins to drain. Include proper units. b. Make an educated guess (as good as you can get with the data provided) of the instantaneous rate of change in volume at 15 minutes. Include the proper units.
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A cylindrical tank contains 100 gallons of water. A plug is pulled from the bottom of the tank and the amount of water in gallons remaining in the tank after $x$ minutes is given by $$A(x)=100\left(1-\frac{x}{5}\right)^{2}$$ (a) Calculate the average rate of change of $A$ from 1 to 1.5 and from 2 to $2.5 .$ Interpret your results. (b) Are the two average rates of change the same or different? Explain why.
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