Problem

Solve \(40(1.5)^t~=~20\) 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: 40(1.5)t = 20 has real solution t = ln(0.5)/ln(1.5) ≈ 1.7095, but it is invalid when t ≥ 0. For nonnegative time the growth model is at least 40.

Analysis: 40(1.5)t = 20 has real solution t = ln(0.5)/ln(1.5) ≈ −1.7095, but it is invalid when t ≥ 0. For nonnegative time the growth model is at least 40.

Analysis: 40(1.5)t = 20 has real solution t = ln(0.5)/ln(1.5) ≈ −1.7095, and it is valid when t ≥ 0. For nonnegative time the growth model is at least 40.

Analysis: 40(1.5)t = 20 has no real solution t = ln(0.5)/ln(1.5) ≈ −1.7095, but it is invalid when t ≥ 0. For nonnegative time the growth model is at least 40.

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Solve \(40(1.5)^t~=~20\) 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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