Step 1 :The domain of a function is the set of all possible input values (independent variable), which in this case is \(T\), the total number of minutes that water has been added. Since the problem states that the function is valid for the next 70 minutes, the domain is all real numbers from 0 to 70.
Step 2 :The range of a function is the set of all possible output values (dependent variable), which in this case is \(W\), the total amount of water in the pond. We can find the minimum and maximum values of \(W\) by substituting the minimum and maximum values of \(T\) into the function \(W=35T+500\).
Step 3 :Substitute \(T=0\) into the function to find the minimum value of \(W\): \(W=35*0+500=500\).
Step 4 :Substitute \(T=70\) into the function to find the maximum value of \(W\): \(W=35*70+500=2950\).
Step 5 :\(\boxed{\text{Domain: number of minutes water has been added, from 0 to 70.}}\)
Step 6 :\(\boxed{\text{Range: amount of water in the pond (in liters), from 500 to 2950.}}\)