Ask Question
13 February, 11:35

2. Assume that the growth rate of a population of ants is proportional to the size of the population at each instant of time. Suppose 100 ants are present initially and 230 are present after 3 days.

a. Write a differential equation that models the population of the ants.

b. Solve the differential equation with the initial conditions.

c. What is the population of the ants after 14 days?

+2
Answers (1)
  1. 13 February, 12:05
    0
    (a) The differential equation that would best represent the given is,

    dP/dt = kP

    (b) Solving the differential equation,

    dP/P = kdt

    lnP - lnP₀ = kt

    Solving for k,

    ln (230) - ln (100) = k (3); k = 0.2776

    (c) Solving for P at t = 14

    ln (P) - ln (100) = 0.2776 (14); P = 4875.99

    The population of the ants after 14 days is approximately 4876.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “2. Assume that the growth rate of a population of ants is proportional to the size of the population at each instant of time. Suppose 100 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers
You Might be Interested in