Why Are Some Speed Limit Signs Yellow?
This is kind of a trick question, because those yellow road signs showing a certain speed in black letters aren't actually speed limit signs. Technically, they're warning signs. That means, according to the Manual on Uniform Traffic Control Devices (MUTCD) — Chapter 1C.02.289 — they're there to give "notice to road users of a situation that might not be readily apparent." More specifically, black-on-yellow speed signs are typically used in two applications: as advisory exit and entry ramp speed signs (2C.12) or advisory speed plaques (2C.59). As for their black-on-yellow color themes, this is mandated in Chapter 1D.05, along with the color meanings of the country's other traffic signs, like green highway signs.
We'll see what distinguishes those advisory signs from each other down below, but first, let's deal with an important difference between both of them and the more common black-and-white regulatory speed limit signs: As their name suggests, the warning signs are just meant to advise drivers, not mandate a legal speed. The regulatory signs indicate the legally regulated speed, as determined by traffic engineers. So, you cannot get a speeding citation specifically for exceeding the posted speeds of an advisory sign.
That said, remember that you can still get a speeding ticket for violating the "basic speed law" in almost any scenario. Section 257.627 of the Michigan Code of Law is typical in mandating that vehicles must be operated "at a careful and prudent speed not greater than nor less than is reasonable and proper, having due regard to the traffic, surface, and width of the highway and of any other condition existing at the time." Needless to say, that can also give cops a pretext for stopping minority drivers.
When are yellow speed limit signs used?
As mentioned, the first case for the yellow advisory speed signs is getting on and off highway ramps, as covered in MUTCD 2C.12. These can be standalone signs, or they can be used in combination with others, and there are strict guidelines on when to deploy them. It comes down to the difference in speed between nearby mainline roads and the appropriate ramp speed. For instance, a black-on-yellow advisory speed sign must be used if the state's traffic engineers call for an advised ramp speed 20 mph higher or lower than the regulatory speed limits of nearby main roads. With differential speeds of 15 mph and 10 mph, the signs are considered recommended and optional, respectively.
The other situation where you might see a speed sign with a yellow background is when it's used in combination with a warning sign for a specific hazard — if you're suddenly coming up to an unexpected sharp turn, you may see black-on-yellow sign with a turn graphic, as well as a second sign with the advised speed for the turn. The MUTCD refers to these as advisory speed plaques in Chapter 2C.59, and ignoring them can be a good way to get into an accident.
Naturally, the MUTCD also provides criteria for when these signs are required. Keeping a sharp curve for our example, you compare a road's "regular" speed limit — whether it's from a statute or the 85th percentile rule — to the engineer-determined advisory speed specifically for the turn. Here, a speed sign is required when the differential is above 15 mph, recommended above 10 mph, and optional above 5 mph.