Combine standard functions using arithmetic operations to build models.
Build a net-change model from inflow and outflow functions
Problem
Water enters a tank at \(I(t)~=~12t\) and leaves at \(O(t)~=~5t\). Write the net-change model for inflow minus outflow.
Big Picture
What this problem is really about
Net change depends on direction: entering contributes positively, while leaving must be removed. We’ll align the inflow and outflow over the same time input, write their difference in meaning-first order, and combine terms with matching units. The sign of the resulting rate then tells whether the stored amount grows or shrinks over time.
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