Problem

Solve \(100(0.8)^t~=~150\) over the reals, then test the result against the contextual restriction \(t~\ge~0\) and explain the model behavior for nonnegative time.

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Analysis: 100(0.8)t = 150 has real solution t = ln(1.5)/ln(0.8) ≈ −1.8171, but it is invalid when t ≥ 0. For nonnegative time the decay model never exceeds 100.

Analysis: 100(0.8)t = 150 has no real solution t = ln(1.5)/ln(0.8) ≈ −1.8171, but it is invalid when t ≥ 0. For nonnegative time the decay model never exceeds 100.

Analysis: 100(0.8)t = 150 has real solution t = ln(1.5)/ln(0.8) ≈ 1.8171, but it is invalid when t ≥ 0. For nonnegative time the decay model never exceeds 100.

Analysis: 100(0.8)t = 150 has real solution t = ln(1.5)/ln(0.8) ≈ −1.8171, and it is valid when t ≥ 0. For nonnegative time the decay model never exceeds 100.

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Solve \(100(0.8)^t~=~150\) over the reals, then test the result against the contextual restriction \(t~\ge~0\) and explain the model behavior for nonnegative time.

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