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The acceleration of a particle is dependent on the velocity according to the equation $a = -bv(t)$.

Assuming that the particle velocity at $t = 0$ is $v = v_0$, what is the velocity of the particle at any time $t$?

$v(t)=-b v_0t$

$v(t)=v_0+ bt$

$v(t)=v_0e^{bt}$

$v(t)= v_0e^{-bt}$

$v(t) = e^{-bt}$