Consider the differential equation \(\frac{{{\rm{dx}}}}{{{\rm{dt}}}} = 10{\rm{\;}}-{\rm{\;}}0.2{\rm{x}}\) with initial condition \({\rm{\;x}}\left( 0 \right){\rm{\;}} = {\rm{\;}}1\). The response x(t) for \({\rm{t}} > 0\) is

\(50{\rm{\;}}-{\rm{\;}}49{{\rm{e}}^{0.2{\rm{t}}}}\)

\(2{\rm{\;}}-{\rm{\;}}{{\rm{e}}^{ - 0.2{\rm{t}}}}\)

\(2{\rm{\;}}-{\rm{\;}}{{\rm{e}}^{0.2{\rm{t}}}}\)

\(50{\rm{\;}}-{\rm{\;}}49{{\rm{e}}^{ - 0.2{\rm{t}}}}\)

Consider the differential equation \(\frac{{{\rm{dx}}}}{{{\rm{dt}}}} =

1.	Consider the differential equation \(\frac{{{\rm{dx}}}}{{{\rm{dt}}}} = 10{\rm{\;}}-{\rm{\;}}0.2{\rm{x}}\) with initial condition \({\rm{\;x}}\left( 0 \right){\rm{\;}} = {\rm{\;}}1\). The response x(t) for \({\rm{t}} > 0\) is
A.	\(2{\rm{\;}}-{\rm{\;}}{{\rm{e}}^{ - 0.2{\rm{t}}}}\)
B.	\(2{\rm{\;}}-{\rm{\;}}{{\rm{e}}^{0.2{\rm{t}}}}\)
C.	\(50{\rm{\;}}-{\rm{\;}}49{{\rm{e}}^{ - 0.2{\rm{t}}}}\)
D.	\(50{\rm{\;}}-{\rm{\;}}49{{\rm{e}}^{0.2{\rm{t}}}}\)
Answer» D. \(50{\rm{\;}}-{\rm{\;}}49{{\rm{e}}^{0.2{\rm{t}}}}\)

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