A quantity doubles every 3 hours, starting at 50. What is the quantity after 9 hours?

The quantity doubles every $3$ hours, so after $9$ hours it has doubled $\frac{9}{3}=3$ times. That is $50\cdot2^3=50\cdot8=400$, choice C. Listing the values shows the pattern: $50$ at hour $0$, $100$ at hour $3$, $200$ at hour $6$, and $400$ at hour $9$. Choice A ($150$) adds $50$ three times, treating the growth as additive. Choice B ($300$) multiplies $50$ by $6$, doubling the number of doubling periods rather than using the exponent. Choice D ($450$) is $50\cdot9$, multiplying by the hours. Doubling is exponential growth, so use powers of $2$.