Consider the Market Model $\begin{array} { l } Q _ { S } = 4 P - 3 \\Q _ { D } = - 2 P + 13 \\\frac { d P } { d t } = 0.4 \left( Q _ { D } - Q _ { S } \right)\end{array}$

Multiple Choice

Consider the market model
$\begin{array} { l } Q _ { S } = 4 P - 3 \\Q _ { D } = - 2 P + 13 \\\frac { d P } { d t } = 0.4 \left( Q _ { D } - Q _ { S } \right) \end{array}$
Find an expression for $Q _ { D } ( t )$ when $P ( 0 ) = 2$ .

A) $\frac { 2 } { 3 } \left( 4 - e ^ { - 2.4 t } \right)$

B) $\frac { 1 } { 3 } \left( 23 + 4 e ^ { - 2.4 t } \right)$

C) $\frac { 1 } { 3 } \left( 4 + e ^ { - 2.4 t } \right)$

D) $\frac { 2 } { 3 } \left( 4 + e ^ { - 2.4 t } \right)$

E) $\frac { 1 } { 3 } \left( 23 - 8 e ^ { - 2.4 t } \right)$