Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.
Write an exponential or logarithmic constraint from a growth context
Problem
Population is \(P(t)~=~1000(1.04)^t\) and must exceed \(2000\) for time \(t~\ge~0\). Write the exponential constraint and feasible time domain.
Big Picture
What this problem is really about
Use the supplied growth model as the population expression, then translate the target wording separately. “Must exceed” is strict, so the boundary value itself does not satisfy the requirement. Pair that inequality with the nonnegative domain for elapsed time; the growth condition alone does not communicate which input values are meaningful in the context.
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