calculus

A population of a very rare insect in an area in a discrete rural region in ASEAN will grow at a rate that is proportional to their current population. In the absence of any outside factors, the population will triple in two weeks’ time. On any given day there is a net migration (into the area) of 15 insects and there are also an extinction cause by identified factor such as 16 are eaten by the local bird population and 7 die of natural causes. If there are initially 100 insects in the area, predict either the population of the rare insect will survive or not? If not, when do they will die out?

  1. 👍 0
  2. 👎 0
  3. 👁 336
  1. Hmmm. If the population is p, then we have

    dp/dt = kp
    dp/p = k dt
    ln(p) = kt + c
    p = c e^kt

    Now we know that p triples in 14 days, so we can forgo using e, and just use 3 as our base:

    p(t) = Po * 3^(t/14)

    so, starting with 100, and gaining 15 per day and losing 23 each day, making a net loss of 8 per day.

    p(t) = 100*3^(t/14) - 8t

    so, take a look at the graph and decide:

    http://www.wolframalpha.com/input/?i=100*3^%28t%2F14%29+-+8t

    1. 👍 0
    2. 👎 0
  2. 34

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Educational Technology

    What does it mean to say that a country's land area is positively correlated with its population? a) The larger the land area of a country, the higher its population tends to be. b) The smaller the land area of a country, the

  2. World Geography

    1.Which of the following demographic characteristics distinguishes Europe's population from that of Asia? A.) More Europeans inhabit rural areas. B.) The European population is much younger. C.) Europeans are more concentration in

  3. MATH

    A population of insects increases at a rate of 250 + 16t +0.3t^2 insects per day. Find the insect population after 3 days, assuming that there are 40 insects at t=0.

  4. College Algebra

    The fox population in a certain region has an annual growth rate of 9% per year. In the year 2012, there were 20,700 foxes counted in the area. What is the fox population predicted to be in the year 2020? Round to the nearest fox.

  1. Science

    A particular ecosystem in Georgia can support a maximum population of 100 bluebirds which of the following would allow hundred 20 bluebirds to live together in this ecosystem? (a. Human activity disrupting the nesting out of a

  2. calculus

    Sketch the region enclosed by the curves x=64−y^2 and x=y^2−64. Decide whether to integrate with respect to x or y. Then find the area of the region. Area =

  3. social studies

    Which of the following is a reason so many people have migrated from Middle America to other regions? A.They dislike the region's climate. B.They want to gain an education. C.They hope to escape poverty.**** D.They want to live

  4. history

    How has Mexico’s population changed in recent decades? A. Due to migration, the population has decreased. B. More people have moved from the highlands to the coasts. C. The bulk of the population has shifted from rural to urban.

  1. Algebra 1 Math

    an insect flies 20ft in 1 s. how fast does the insect fly in miles per hour?

  2. Geography of Arabia and Iraq

    Question #1: Which statement best describes the physical geography of Arabia and Iraq? A. largely hot and dry with pockets of mountains and fertile river valleys B. tropical, with equal parts rainforest and desert C. mountainous,

  3. Physics

    A bat moving at 5 meters per second is chasing a flying insect, if the bat emits a 40 khz chirp and receives back an echo at 40.4 khz what is the speed of the insect and will the bat be able to catch the insect?

  4. biology

    A farmer sprays insecticide on his crops and notices that the insect pest problem disappears. A year later he tries the same insecticide only to find that he did not achieve the same result. The insect population shows resistance

You can view more similar questions or ask a new question.