Answer:
Rate of change of water will be -6 gallon/minute
Explanation:
We have given water in the tank as the function of time as
[tex]w(t)=25-t^2[/tex]
We have to find the rate of change of water in the tank at t = 3 minute
For rate of change we have to differentiate both side
So [tex]\frac{dw}{dt}=0-2t[/tex]
At t = 3 minute
[tex]\frac{dw}{dt}=0-2\times 3=-6gallon/minute[/tex]
The rate at which the gallons is changing in gallons per minute is -6 gallons per minute.
In the question, we are told that the number of gallons is changing with respect to time. This means that we can model the change in the number of gallons with respect to time by [tex]\frac{dw}{dt} [/tex].
Hence;
[tex]\frac{dw}{dt} = -2t[/tex]
When we substitute values, we arrive at the value;
[tex]\frac{dw}{dt} = -2(3) = -6 gallons/min[/tex] ( at t = 3 minutes).
Hence, the rate at which the gallons is changing in gallons per minute is -6 gallons per minute.
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