Problem

Tank volume \(V(t)\), in gallons, has average rate of change \(-3~\text{gallons}~\text{per}~\text{minute}\) from \(t~=~0\) to \(t~=~10~\text{minutes}\). Calculate the input and output changes, state the units, and interpret the average rate and total change in context.

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input change = 10-0=10 minutes; average rate = -3 gallons/minute; output change = -3·10=-30 gallons; meaning = over minutes 0 to 10, volume decreases 30 gallons total, averaging a loss of 3 gallons per minute

input change = 10 minutes; rate = -3 gallons/minute; output change = -3 gallons total

input change = 10 minutes; rate = +3 gallons/minute; output change = +30 gallons

input change = 10 minutes; rate = -3 minutes/gallon; output change = -10/3 gallons

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Tank volume \(V(t)\), in gallons, has average rate of change \(-3~\text{gallons}~\text{per}~\text{minute}\) from \(t~=~0\) to \(t~=~10~\text{minutes}\). Calculate the input and output changes, state the units, and interpret the average rate and total change in context.

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