A poster is 16 inches longer than it is wide. Find a function that models its area \( A \) in terms of its width \( w \). \( A(w)=\square \)

To model the area \( A \) of the poster in terms of its width \( w \), we can establish the relationship between the width and the length. Since the poster is 16 inches longer than it is wide, we can express the length as \( w + 16 \). Therefore, the area \( A \) can be calculated using the formula for area \( A = \text{length} \times \text{width} \). Substituting the expressions, we get: \[ A(w) = w(w + 16) = w^2 + 16w. \] So, the function that models the area is \( A(w) = w^2 + 16w \). One common mistake when creating functions like this is to mix up the addition and multiplication of the dimensions. Always double-check that you're correctly interpreting "longer" or "shorter" in relation to the two dimensions of the object! Keeping track of the relationships ensures your function accurately reflects the situation.