$L(8)$ means you plug $t=8$ into the function. Is 8 the time or the luminosity? Is the result the time or the luminosity?

Turn "$L(8)=3.2$" into a plain English sentence: "When the time is __, the luminosity is __." Then compare that sentence to each answer choice.

In Desmos, type L(t) = -0.04t^2 + 0.8t + 6. This defines the function $L(t)$.

In a new line, type L(8) or use a table (click the gear icon next to the function and add a table, then enter 8 in the $t$ column). Look at the corresponding output value; that number is the luminosity (in watts) when $t=8$ hours.

From the problem:

• $t$ is time in hours after the bulb is switched on.
• $L(t)$ is the bulb’s luminosity in watts at that time.

So $L(t)$ does not represent total energy or a rate per hour; it represents the brightness (luminosity) at a particular moment $t$.

The expression $L(8)$ means: the value of the function $L$ when $t=8$.

In words, that is "the bulb’s luminosity 8 hours after it is switched on." The number you get when you evaluate $L(8)$ will be in watts, because $L(t)$ outputs watts.

The equation $L(8)=3.2$ tells you exactly what $L(8)$ equals:

• Input: $t=8$ hours after the bulb is turned on.
• Output: $L(8)=3.2$ watts of luminosity at that time.

So in a sentence, this equation says that 8 hours after being switched on, the bulb’s luminosity is 3.2 watts, which corresponds to answer choice C.