In the absence of rodent herbivores,the per capita population growth rate of a plant in a certain area is 0.06 per year.After the arrival of a population of 500 rodents,the per capita growth rate is -0.02.Assuming that the effect of the rodents on the plants is linear,what is the maximum number of rodents that could be in the area and still allow the plants to have a positive population growth rate?

Question

Quizplus · Accepted Answer

Let R be the number of rodents in the area. Then the per capita growth rate of the plant is given by:

r(R) = 0.06 - (0.06 + 0.02)/500 R
       = 0.06 - 0.00016 R

For the plant to have a positive population growth rate, r(R) > 0, which implies:

0.06 - 0.00016 R > 0

Solving for R, we get:

R < 0.06/0.00016
  = 375

Therefore, the maximum number of rodents that could be in the area and still allow the plants to have a positive population growth rate is 374. Any value of R greater than 374 would make the per capita growth rate of the plant negative.

In the Absence of Rodent Herbivores,the Per Capita Population Growth