# Plot a function which depends on itself

How can I plot a stepwise function like f[a, t] = 10 Exp[-0.1 Sin[t]] for a > t and f[a, t] = f[a, t - 1] Exp[-0.1 a] for a < t? If you see, for a < t, the function f[a, t] dependes on a previous value of itself.

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Two defintions of f, one each side of a.

f[a_?NumericQ, t_?NumericQ] /; a > t := 10 Exp[-0.1 Sin[t]];
f[a_?NumericQ, t_?NumericQ] /; a <= t := f[a, t - 1] Exp[-0.1 a];


Plot it.

Plot[f[5, t], {t, 0, 10}]


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@m_goldberg - Thanks, one day I will figure out how to do that :) – Ymareth Mar 26 '14 at 15:12

I can't understand your question, what is "sent" etc. but try this for a starting point

Manipulate[Plot[Piecewise[{{1 + 3 a, a <= t}, {10 Exp[-0.1 a*20], a > t}}], {a, 0, 2}], {t, 0, 2}]

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Sorry..the question was:How can I plot a stepwise function like f[a,t]= 10exp(-0.1sent) for a>t, f[a,t-1]exp(-0.1a) for a<t....if you see for a<t the function depends on the previous value of the function f[a,t]. – Salvatore Calabrese Mar 26 '14 at 14:32
Still don't understand. You have "sent" in your code which you have not defined. – Ymareth Mar 26 '14 at 14:45
sorry I meant sin[t].. – Salvatore Calabrese Mar 26 '14 at 14:53