A student models the tray data with the quadratic $A(s)=1.04s^2-0.13s-0.82$. According to this model, what usable area is predicted for $s=4.5$ dm?

Answer and derivation

Correct answer: B

The model gives approximately $19.7$ square decimeters.

1. Enter $1.04(4.5)^2-0.13(4.5)-0.82$.
2. The unrounded output is $19.655$.
3. Rounded to the nearest tenth, the prediction is $19.7$ dm$^2$.

Why the other options fail

A

This omits or mis-enters a model term.

B

Correct substitution and rounding.

C

This uses $1.04(4.5)^2$ alone.

D

This copies the observed value at $s=5$.

Common misconception: A model prediction must use the complete equation and stated rounding.

China/AP bridge: AP calculator work still requires reporting the model output with units and reasonable precision.