solve q+(2^(q-2))=t in terms of q

Yeah.....I keep getting q= (((lnt/ln2)+2)/2))
But it doesn't work out when I plug numbers back into it.....

 

so 2^(q-2) = (q-2) x ln2

yeah then on the other side = lnt

q+(q-2) ln2= lnt

q+(q-2) = lnt/ln2

yeah, then idk...

 

Top Secret! lol
In a sense I'm trying to determine my MSY (maximum sustainable yield), maximum efficiency yield actually. I'm assuming that gross production is a function of circumference, and with that assumption I've calculated the growth rate of my cyphestera (metorshower) and tried to determine if there was a difference in production per square inch (effort) based on the starting size of the mother colony. I determined the maximal amount of annual production as a function of the diameter. Second I constrained this data according to the proportions of my frag tank and correlated the maximum % production capacity on one y axis against, maximum possible production on another y axis, both underscored by size of the mother colony. The intersection of these two y axises is an optimization, and the other values associated with this intersection is the $/year, # of species, % value of how hard I'm pushing a species to perform (and of course % value of how much potential I'm loosing from any given mother colonies based on the 2D component of the frag tank). What's really cool is that I'm building these into an excel spread sheet where I can manipulate numerous parameters.

I'd love to see any data you have so that I can corroborate growth rates, get a good average, and compare species and different genera. Conditions and parameters will be added once they can be tested empirically, I'm not going to assume on those variables since I don't have hard data for them, only simply using observed conditions and I'll work out the modifications later.

 

This is getting somewhere now.....I've been mashing my brain up on this problem all weekend. This helps a lot! Back to the drawing board (btw I was aware however that ln a+b is not equal to ln a + ln b, but I had a feeling that I might have not done the operation correctly in light of the correct identity; ln (q+t)= ln q + ln (1 + t/q)
hmmmm

 

can you show your work kylie? lol this one seems crazy to me since there are no real numbers to begin with lol

 

That identity complicates things further....

ln q + ln (1+ ((2^(q-2))/q)= ln t

 

lol old trig note book! I knew keeping that chicken scratch would come in handy!

 

Yeah! I've been pounding out this one for the last two days at breakfast lunch and dinner and I just cannot figure it out. I've killed like 20 sheets of paper trying to figure it using different identities, I even tried to integrate some terms but no avail.