Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.4 Logarithms, #67 · Calculus · Differentiation rules

An ant crawls at 1 foot/second along a rubber band whose original…

An ant crawls at 1 foot/second along a rubber band whose original length is 2 feet. The band is being stretched at 1 foot/second by pulling the other end. At what time $T$ , if ever, does the ant reach the other end?
One ant: The band's length at time $t$ is $t + 2$ . Let $y (t)$ be the fraction of that length which the ant has covered, and explain
(a) $y^{'} = 1/ (t + 2)$ (b) $y = ln (t + 2) - ln 2$ (c) $T = 2 e - 2$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.4 Logarithms, #67

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