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?

Question

Mathematics

Fernanda Banks

5 February, 07:53

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?

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Answers (1)

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Tex · Answer 1

(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.