Final answer:
The net change between the given values of the variable is 12h+2h^2.
Step-by-step explanation:
To determine the net change between the given values of the variable, we need to subtract the initial value from the final value. In this case, the initial value is f(3) = 2(3)^2 = 2(9) = 18 and the final value is f(3+h) = 2(3+h)^2. Substituting t = 3+h into the equation gives f(3+h) = 2(3+h)^2 = 2(9+6h+h^2) = 18+12h+2h^2.
Therefore, the net change between the given values is f(3+h) - f(3) = (18+12h+2h^2) - 18 = 12h+2h^2.