Problem

For \(I(t)~=~I_{0}(1.04)^t\), solve for the time when \(I~=~2I_{0}\). Give the logarithmic expression and decimal time, then state the first completed whole year at or above the threshold.

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What this problem is really about

Separate the continuous crossing time from the first completed reporting period. Cancel the positive initial amount, solve the resulting growth-factor equation with logarithms, and keep its decimal as the exact point where the curve meets the threshold. Then test the neighboring whole years and use the first one actually at or above the target.

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Analysis: (1.04)t = 2, so t = ln(1.04)/ln(2) ≈ 0.0566 years. The first completed whole year at or above double is year 18.

Analysis: (1.04)t = 2, so t = ln(2)/ln(1.04) ≈ 17.7 years. The first completed whole year at or above double is year 18.

Analysis: (1.04)t = 2, so t = ln(2)/ln(1.04) ≈ 17.7 years. The first completed whole year at or above double is year 17.

Analysis: (1.04)t = 2, so t = 2/1.04 ≈ 1.9 years. The first completed whole year at or above double is year 18.

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For \(I(t)~=~I_{0}(1.04)^t\), solve for the time when \(I~=~2I_{0}\). Give the logarithmic expression and decimal time, then state the first completed whole year at or above the threshold.

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