A light bulb's brightness is reduced when placed behind a screen. The amount of visible light produced by the light bulb decreases by 25% with each additional layer that is added to the screen. With no screen, the light bulb produces 750 lumens. The lumen is a unit for measuring the total quantity of visible light emitted by a source.

Question

Select the correct equation that can be used to represent the lumens, L, after x screen layers are added.

A.
L = 750(0.975)x
B.
L = 750(1.25)x
C.
L = 750(0.75)x
D.
L = 750(0.25)x

Answer 1

To determine the correct equation that represents the lumens, \( L \), after \( x \) screen layers are added, we need to analyze the information given:

1. The initial brightness of the light bulb is 750 lumens with no screen.
2. Each layer of the screen reduces the visible light by 25%. This means that 75% of the light is transmitted through each layer.

If 25% of the light is blocked by the screen, then 75% remains. Therefore, after one layer, the light intensity is reduced to:

\[ L = 750 \times (1 - 0.25) = 750 \times 0.75. \]

After two layers, the light intensity would again be reduced by 25% of the remaining light after the first layer, resulting in:

\[ L = 750 \times (0.75) \times (0.75) = 750 \times (0.75)^2. \]

Continuing this for \( x \) layers, the general formula becomes:

\[ L = 750 \times (0.75)^x. \]

Thus, we can see that none of the listed options match this exponentiation form directly, but recognizing that the choice options can take different forms, we must find the one that aligns with \( (0.75)^x \).

Looking at the provided answers:

A. \( L = 750(0.975)^x \)
B. \( L = 750(1.25)^x \)
C. \( L = 750(0.75)^x \)
D. \( L = 750(0.25)^x \)

The correct choice that represents the relationship of lumens after \( x \) screen layers added is:

C. \( L = 750(0.75)^x \).