Final answer:
Eli Whitney's introduction of interchangeable parts was instrumental in advancing the gun culture, leading to the manufacturing innovations by Samuel Colt that revolutionized the firearms industry.
Step-by-step explanation:
The relationship between Eli Whitney's interchangeable parts, the gun culture, and Samuel Colt is best described by stating that Eli Whitney's system of interchangeable parts played a pivotal role in the advent of the gun culture in America, which in turn was revolutionized by the innovations of Samuel Colt. Whitney's idea significantly diversified the production of firearms by making the parts standardized, which not only dropped costs but also made weapons more reliable and easier to repair. Later, Samuel Colt further took advantage of these manufacturing techniques and in doing so, greatly influenced the growth of the firearms industry.