Continuous Time Function

[sooyewguan]

Lets say I have an equation,

y=\alpha e^{\beta W}

where,
\alpha = a e^{b f} and \beta = c f + d

W = \int^{T}_{0}f dt

My problem now is, what happen if f is changing with time t, f(t)

How do I modify my main equation, y, so that it become an continuous-time function, y(t).

Thank you.

[HallsofIvy]

I'm not sure what you mean: what you give
y= \alpha e^\beta W(t)[/itex]
is a "continuous-time function"- or at least a continuous function of t.

If you want to you can replace each of \alpha, \beta, and W with their explicit dependence on t:
[tex]y(t)= ae^{bf(t)} e^{(cf+d)\int_0^t f(u)du}
(I've changed the dummy variable in the integral to u so as not to confuse it with the variable t.)

But I don't think that really adds anything as long as you don't know the explicit form of f.