Problem

For \(y~=~200(0.8)^x\), where \(x\) is continuous time in days beginning at \(0\) and \(y\) is amount remaining, state the algebraic domain and range, contextual domain and range, and boundary meaning.

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Algebraically, x is any real number and y>0. In context, x>=0 and 0<=y<=200. Boundary meaning: the amount eventually reaches and remains at 0.

Algebraically, x is any real number and y>0. In context, x is any real number and y>0. Boundary meaning: negative time is feasible, so there is no initial-time restriction.

Algebraically, x is any real number and y>0. In context, x>=0 and y>=200. Boundary meaning: the model begins at (0,200) and grows above 200.

Algebraically, x is any real number and y>0. In context, x>=0 and 0<y<=200. Boundary meaning: the model begins at (0,200) and approaches 0 without reaching it.

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For \(y~=~200(0.8)^x\), where \(x\) is continuous time in days beginning at \(0\) and \(y\) is amount remaining, state the algebraic domain and range, contextual domain and range, and boundary meaning.

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