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AP Calculus AB/Unit 8: Applications of Integration
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Solving for Time from a Displacement Integral

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The displacement, s(T)s(T), of a particle over the time interval [0,T][0, T] is given by s(T)=∫0T3e−tdt=3(1−e−T)s(T) = \int_0^T 3e^{-t} dt = 3(1 - e^{-T}). Find the time TT at which the displacement is 2.12.1.

A

−ln⁡(0.3)-\ln(0.3)

B

−ln⁡(0.7)-\ln(0.7)

C

ln⁡(0.3)\ln(0.3)

D

ln⁡(2.1)\ln(2.1)

E

−ln⁡(2.1)-\ln(2.1)

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