Question

In: Advanced Math

One method of slowing the growth of an insect population without using pesticides is to introduce...

One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. Let P represent the number of female insects in a population and S the number of sterile males introduced each generation. Let r be the per capita rate of production of females by females, provided their chosen mate is not sterile. Then the female population is related to time t by

t =

P + S
P[(r − 1)PS]
  dP.

Suppose an insect population with 10,000 females grows at a rate of

r = 1.8

and 700 sterile males are added. Evaluate the integral to give an equation relating the female population to time. (Note that the resulting equation can't be solved explicitly for P. Remember to use absolute values where appropriate.)

Solutions

Expert Solution

Therefore the equation is determined as shown above.


Related Solutions

An economy is described by the standard Solow model without technological progress and without population growth....
An economy is described by the standard Solow model without technological progress and without population growth. You are given the information that the savings rate dropped to a lower level in this economy, but you don’t know by how much it did so. Suppose that prior to the drop in s the economy was in a steady-state with a capital stock per worker higher than the Golden Rule level. a. In a graph which should include the production function, the...
An economy is described by the standard Solow model without technological progress and without population growth....
An economy is described by the standard Solow model without technological progress and without population growth. You are given the information that the savings rate dropped to a lower level in this economy, but you don’t know by how much it did so. Suppose that prior to the drop in s the economy was in a steady-state with a capital stock per worker higher than the Golden Rule level. a. In a graph which should include the production function, the...
Consider an economy in steady state (or on a “balanced growth path”)without population growth. Suppose that...
Consider an economy in steady state (or on a “balanced growth path”)without population growth. Suppose that a mysterious new disease (COVID-19) suddenly kills half of the population. We are interested in the effect this likely has on kapital and output per person , both in the short and the long run. How will this affect in the Solow-model? Show with a graph
Without any controls, population growth would be exponential. However, this does not occur because there are...
Without any controls, population growth would be exponential. However, this does not occur because there are population-limiting factors.Describe the growth pattern of populations growing in a limited environment..What is meant by density-dependent factors that affect growth Give three examples of density-dependent factors and explain how they affect population growth. Give one example of a density-independent (abiotic) factor that affects growth and explain why it is density independent.
Describe the mechanisms by which meiosis would introduce genetic variability in a population. If one diploid...
Describe the mechanisms by which meiosis would introduce genetic variability in a population. If one diploid yeast cell was heterozygous for an allele with a Dominant mutation on it, what proportion of its offspring could be expected to carry that dominant mutation after mating? (Assume it mates with a cell that is homozygous for the normal, recessive allele.) Interestingly, yeast switch to sexual reproduction when they are under conditions of stress. For the purposes of this task, assume yeast populations...
What is the difference between the population growth of the predators without prey (N0=0), versus prey...
What is the difference between the population growth of the predators without prey (N0=0), versus prey growth without predators (P0=0)?
Using a standard Solow growth model with population growth, describe the evolutions of the real wage,...
Using a standard Solow growth model with population growth, describe the evolutions of the real wage, the real rental rate of the physical capital and the aggregate physical capital real income when an economy accumulates more physical capital per worker.
Using the logistic equation (S-shaped curve), calculate population growth in one year when K = 1,000,...
Using the logistic equation (S-shaped curve), calculate population growth in one year when K = 1,000, N=100, r=0. Please show me how to calculate it! 0 100 35 1.00 0 0 1 65 ? 0.65 0 0 2 45 15 ? 3 1.35 3 30 20 0.30 1 ? 4 10 10 0.10 1 0.10 5 0 0 0.00 1 0
one factor that contributed to the growth in share of population employed in the U.S. between...
one factor that contributed to the growth in share of population employed in the U.S. between 1960 and 1980 was increased by
Using the Solow model, illustrate and explain why a nation with a higher population growth        ...
Using the Solow model, illustrate and explain why a nation with a higher population growth         rate might have a lower per capita GDP than a comparable nation with a lower rate of            population growth.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT