Growth rates are dependent on a variety of factors. Sunflowers grow fast for sure, but that is also under ideal conditions. The growth rate of any individual member of a species or the population number of a species within an ecosystem is dependent on some limiting factors. For a sunflower, those things could be (but not limited to) soil health, soil amount, temperature, humidity, wind, water amount, water purity, absence of harmful biologicals (rodents, birds, bacteria, virus, etc.), and sunlight.
Sunflower growth rate and population density growth rates both tend to follow a logistic growth curve when the data is shown in graph format. A logistic growth curve has four phases. Phase 1: steady slow growth. Phase 2: rapid, exponential growth. Phase 3: growth begins to slow. Phase 4: Steady state. This is where a population's average will be. For a sunflower, this will be it's average max height.
Sunflowers tend to grow very rapidly for the first 50 days (7 weeks). The growth slows over the next 4 weeks and then tops out around 12 weeks at an average height of about 275 - 365 cm (9-12 feet)
I was able to find a study done in 1919 by Reed and Holland that tracked sunflower growth by week. I've attached a link that summarizes their data and presents it in table format and graphs the data as well. I hope that it helps!