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How can I substitute an unknown function in an expression with a known function?

I have defined an unknown function "p" with command

p=function("p")

Then I deduced another function, which contains "p":

aws(time)=921600*(-1333.33340000000*time + 2000)/(-3.36000004800000e6*p(time) + 3840000)

Now I would like to plot the function aws(time), by subtituting p(time) with a known function, like:

p(time)=time^0.54

I discovered I can't use .subs() as with free variables, so this doesn't work:

 aws.subs(p(time)==time^0.54)

Then how can I substitute the known function, to be able to plot aws(time) finally?