Which of the Following Gives the Solution of the Difference $Y _ { t } = b Y _ { t } - 1 + c$

Multiple Choice

Which of the following gives the solution of the difference equation
Yt = bYt - 1 + c, With initial condition, Y0 = a?
$Y _ { t } = b Y _ { t } - 1 + c$ , with initial condition, $Y _ { 0 } = a$ ?

A) $\frac { c ( 1 - a + c ) b ^ { t } + c } { 1 - b }$

B) $\frac { c \left( 1 - b ^ { t } \right) } { 1 - b } + a b ^ { t }$

C) $\frac { a ( 1 - c ) b ^ { t } + a b } { 1 - b }$

D) $\frac { c b ^ { t } } { 1 - b } + a ( 1 - b )$

E) $\frac { a ( 1 - b + c ) b ^ { t } + c } { 1 - b }$