Math problem (for one CIV-like game)?

Question

Mathematics

Good evening, dear Khabrovites, let me introduce you to solve one interesting problem for one CIV-like game:
Given:
p - population
i - population growth per hour
r - resource volume in the warehouse
k - resource consumption coefficient (each person consumes k resource)
d is the production factor (to get the real production run: d*(10+p^0.85) )
All values ​​> 0
Find:
In how many hours (t) will the consumed resource end?
If a solution cannot be found, it must be proven.

Answer 1

The integral of the curve is obtained, and so - what is particularly interesting there? ..

Answer 2

Em. Sounds more like computer science homework, doesn't it?

Answer 3

Hold on - dl.dropbox.com/u/12130795/problem.pdf

Answer 4

r-(p+i*t)*k*t+(d*(10+(p+i*t)^0.85))*t=0
But I doubt it. Not entirely clear with the production factor

Answer 5

If I understand the conditions correctly, I will redefine the variables a bit:
p0- initial population
r0- initial resource
(1) Population formula: p=p0+it
(2) Food formula: r=r0+d(10+p ^0.85)t
(3) End of food expression: r-kp=0
Substitute (1) and (2) into (3):
(r0+d(10+p^0.85)t)-k(p0+it)= 0
Simplify and allocate time:
r0+d(10+p^0.85)t-kp0-kit=0
r0-kp0=kit-d(10+p^0.85)t
r0-kp0=(ki-d(10+p ^0.85)t
Something like this: t=(r0-kp0)/(ki-d(10+p^0.85)
Substitute the data, check.

Answer 6

Yes, it's only a matter of numbers.
And yes, I completely agree that such tasks are easier to solve after all by modeling.