Which function models intensity $I(p)$ after $p$ panels are installed?

Answer and derivation

Correct answer: C

The initial value is 960 and each panel retains 75% of the preceding intensity.

1. At $p=0$, intensity is 960 lux.
2. Every equal panel step has ratio $0.75$.
3. Therefore $I(p)=960(0.75)^p$.

Why the other options fail

A

The differences are not constant.

B

It uses the 25% loss as the retained factor.

C

Correct initial value and factor.

D

It shifts the initial value to the one-panel output without shifting the exponent.

Common misconception: Percent removed and percent remaining play different roles in an exponential model.

China/AP bridge: China-course bridge: percent change and geometric sequences are familiar; AP requires constructing a contextual function and interpreting parameters; unlike a fixed-decrease model, use equal-interval ratios; avoid dropping units or using 0.25 as the multiplier.