Population growth (doubling each hour): starting with 50 bacteria, how many are born during the 12th hour?

Introduction / Context:
For exponential growth that doubles each hour, the population after n hours is P(n) = P(0)*2^n. The “born during the nth hour” equals the increment from hour n−1 to hour n.

Given Data / Assumptions:

• Initial P(0) = 50.
• Doubling every hour: P(n) = 50*2^n.
• We seek births in the 12th hour: P(12) − P(11).

Concept / Approach:
Compute the increment as P(12) − P(11) = 50*2^12 − 50*2^11 = 50*2^11.

Step-by-Step Solution:
2^11 = 2048.Births in 12th hour = 50 * 2048 = 102,400.

Verification / Alternative check:
Interpretation check: “born in the 12th hour” means increase during that hour, not total to date or population at the end.

Why Other Options Are Wrong:
120,400 and 120,450 correspond to misapplied exponents; 102,460 is a rounding-like error (incorrect power or addition).

Common Pitfalls:
Using 2^12 instead of 2^11 for births; answering with total population at hour 12 rather than births during that hour.

Final Answer:
102400