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Clarify whether growth is compounded annually or simple, then derive the formula for compound growth: final = initial * (1 + rate)^t. Discuss edge cases like rate = 0, t = 0, and negative rates, and mention how to handle non-integer t or continuous compounding if relevant.
Pro tip: Show awareness of numerical precision and potential overflow for large t, and suggest using logarithms or iterative multiplication with early termination for efficiency. Also, relate the problem to real-world scenarios like user base growth or financial projections to demonstrate product thinking.
Ask if the growth is compounded annually, if the rate is constant, and if t is an integer number of years. Confirm whether simple or compound interest logic applies.
For compound growth, use final = initial * (1 + rate)^t. Explain that this models exponential growth, and note that for simple growth it would be initial * (1 + rate * t).
Discuss scenarios like rate = 0 (no growth), t = 0 (initial value), negative rates (decay), and non-integer t (e.g., months). Mention that for continuous compounding, use initial * e^(rate * t).
If coding, choose between iterative multiplication (O(t)) and using Math.pow (O(1) but potential precision issues). For large t, use logarithms to avoid overflow, and consider rounding for employee counts.
Test with small examples (e.g., initial=100, rate=0.1, t=2). Discuss how to extend to varying rates or contributions, and relate to real-world metrics like user growth or revenue.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.