A logistic growth model problem?

Question

Can someone help me with this problem? I will give 10 points to the person who gives the most clear response.

Suppose that in a population growing according to the logistic growth model, we have P5= 10/28 and P6= 20/28. Find r.

Answer 1

PLEASE READ IT COMPLETLY
i'am a 9th grade student and donno much about these problems but i think the answer is 100% because if P=POPULATION AND R=RATE then population ant fifth year is 10 persons per 28 kilometers then it is 20 persons per 28 kilometers and the rate of increase of population is 100%

Answer 2

Hi. This was interesting. A formula for unconstrained growth (as in no food limits or other limits) is just dP/dt = rP (Population delta / time delta = rate of population growth). Makes sense. But logistic growth (one where some limits are hit) needs a correction factor that is modified by the population size. If you set a MAXIMUM population to some value (K in the formula I saw on the web) than the rate of population growth (rP) is multiplied by this correction factor (1- P/K). As the population gets closer to K, the influence of the correction becomes stronger. Where P=K you have 1-1 (or zero) multiplied by rP, which then becomes zero as well. Pretty neat, no?

Answer 3

Lets say the population starts at year 1 with p0; at the end of t he first year it will be p0(1+r), where r is the fractional increase each year (0.7191). The next year it will be [p0(1+r)]*(1+r); year 3 it will be p0*(1+r)*(1+r)*(1+r) now you can see the pattern: at the end of n years, the population will be p0(1+r)^n