I can see we're working on this exponential growth problem - these bacteria doubling questions can definitely be tricky if you don't approach them systematically. Let me walk you through the core logic here.
Here's how to think about this step by step:The key insight you need to grasp is that "doubles every 2 minutes" means we multiply the population by 2 after each 2-minute interval. So let's track this progression:
Step 1: Set up the doubling patternStarting point (Time = 0): 1,000 bacteria
Step 2: Track the growth systematicallyAfter 2 minutes: \(1,000 \times 2 = 2,000\)
After 4 minutes: \(2,000 \times 2 = 4,000\)
After 6 minutes: \(4,000 \times 2 = 8,000\)
After 8 minutes: \(8,000 \times 2 = 16,000\)
After 10 minutes: \(16,000 \times 2 = 32,000\)
After 12 minutes: \(32,000 \times 2 = 64,000\)
After 14 minutes: \(64,000 \times 2 = 128,000\)
After 16 minutes: \(128,000 \times 2 = 256,000\)
After 18 minutes: \(256,000 \times 2 = 512,000\)
Step 3: Find when we exceed the targetNotice that at 16 minutes we have 256,000 bacteria (still below 500,000), but at 18 minutes we have 512,000 bacteria (which exceeds our target of 500,000).
Since the problem asks "approximately how many minutes," and we need to reach 500,000, we need 18 minutes to get there.
Answer: (E) 18The critical thing to understand here is that growth happens at discrete 2-minute intervals - we can't have partial doublings, so we need to find the first time point where we meet or exceed the target.
For the complete systematic framework that works for all exponential growth problems, plus the time-saving techniques and common variations you'll see on the GMAT, you can check out the
detailed solution on Neuron. You'll also find comprehensive explanations for
similar official questions with step-by-step approaches that help you master these patterns consistently.