Question 294714: The amount of water in a bathtub can be modeled by the function w(t)=5t where t is the time in minutes and w(t) is the amount of water left in the bathtub. What is a reasonable domain and range for w(t)? explain I don't understand at all
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! The amount of water in a bathtub can be modeled by the function w(t)=5t where t is the time in minutes and w(t) is the amount of water left in the bathtub. What is a reasonable domain and range for w(t)? explain I don't understand at all
Note that water is running out of the tub starting at time 0 when the tub is full.
The range of a function is the set of values that the function can take on. Since the function w(t) represents the quantity of water left in the bath tub after t seconds have elapsed, the range of w then would be set of values between zero (when the tub is empty) and the amount of water in the full tub. Let's say that value is F (for full).
The domain of the function w(t) is that set of values that the "independent" variable, in this case t, can take on. w(t) is the dependent variable since it depends on the value of t.
At time t=0 the tub is full and at some future time say t=T, the tub is empty. The domain for the function then is the set of values between 0 and T.
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