SOLUTION: Given the population of rabbit in human habitat (rabbit farm) grows at a rate proportional to the number of rabbit at time {{{y}}} (year). It is observed that 200 and 800 rabbits a

Algebra ->  Equations -> SOLUTION: Given the population of rabbit in human habitat (rabbit farm) grows at a rate proportional to the number of rabbit at time {{{y}}} (year). It is observed that 200 and 800 rabbits a      Log On


   

Question 1058845: Given the population of rabbit in human habitat (rabbit farm) grows at a rate proportional to the number of rabbit at time y (year). It is observed that 200 and 800 rabbits are presented at 3rd year and 6th year respectively. What was the initial number of the rabbit, y%280%29=y0 ? How long does it take the population to double to 2y0 ?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The same variable MUST be used for one single countable or measurable quantity. It must not be used for two different meanings.
Pick either y for population or y for time - NOT both.

y may be used for number of years after time year 0.
p for population.

Start the possible growth model as p=p%5Bo%5D%2Ae%5E%28ky%29.
ln%28p%5Bo%5D%29%2Bky=ln%28p%29
ln%28p%29=ky%2Bln%28p%5Bo%5D%29------this is a LINEAR equation.
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Form your linear system of equations using two points, (3, ln(200) ), and (6, ln(800) ).
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system%28ln%28200%29=k%2A3%2Bln%28p%5Bo%5D%29%2Cln%28800%29=k%2A6%2Bln%28p%5Bo%5D%29%29
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highlight%28system%283k%2Bln%28p%5Bo%5D%29=5.2983%2C6k%2Bln%28p%5Bo%5D%29=6.6846%29%29
Here, you can use elimination method to solve for the two unknown variables system%28ln%28p%5Bo%5D%29%2C+and%2C+k%29.