The voltage VVV (in mV) in a biological sensor over time ttt (in ms) is modeled by the function V=V(t)V = V(t)V=V(t). The curve C C\,C with equation V=V(t)V = V(t)V=V(t) is described by the following features:
State the equation of the horizontal asymptote to the curve with equation y=V(−t)y = V(-t)y=V(−t).
State the coordinates of the maximum turning point on the curve with equation y=V(2t)y = V(2t)y=V(2t).
Given that the horizontal line V=kV = kV=k, where k k\,k is a constant, intersects C C\,C at exactly one point:
Determine the possible values for kkk.
The curve C C\,C is transformed to a new curve that passes through the origin.
(i) Given that the new curve has equation y=V(t)−cy = V(t) - cy=V(t)−c, state the value of the constant ccc.
(ii) Write down an equation for another single transformation of C C\,C that also results in a curve passing through the origin.
