Question #496b1

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Answer 1 · 2017-08-14T20:16:48

# 100e^(-0.2t).#

Given that, #(dN)/dt=KN.#

# :. (dN)/N=Kdt,.....".[Separable Variable Type Diff. Eqn.]."#

Integrating, #int(dN)/N=Kintdt+C.#

#:. lnN=Kt+C.#

#:. N=e^(Kt+C)=e^(Kt)*e^C=ce^(Kt)," where, c=e^C."#

With, #c=100, &, K=-0.2," we have,"#

#N=100e^(-0.2t).#

Hence, the Last Option is the Right Choice.