Infer time from a remaining fraction

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Problem: Infer time from a remaining fraction
An isolated sample decreases from 80 million undecayed nuclei to 10 million. Its half-life is 3 days.
Question: Find the elapsed time.
Givens:
- N₀ = 80 million
- N = 10 million
- T½ = 3 days
Assumptions: Isolated large radioactive population; constant half-life, no replenishment and no daughter contribution to the stated parent count.
Choices (LaTeX):
A. 6\ \mathrm{days}
B. 24\ \mathrm{days}
C. 9\ \mathrm{days}
D. 3\ \mathrm{days}

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.