In a city having a fixed population of P persons, the time rate of change of the number N of those people who have heard a certain rumor is proportional to the number of those who have not yet heard the rumor. After the rumor was started, a poll found that 15% of the population had heard the rumor after 5 days. Write a differential equation that models this phenomenon with P = 6100000, N (0) = 5600.

Question

Mathematics

Georgia Novak

22 April, 00:34

In a city having a fixed population of P persons, the time rate of change of the number N of those people who have heard a certain rumor is proportional to the number of those who have not yet heard the rumor. After the rumor was started, a poll found that 15% of the population had heard the rumor after 5 days. Write a differential equation that models this phenomenon with P = 6100000, N (0) = 5600.

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Callie York · Answer 1

Answer: The differential equation can be written as;

dN/dt = k (P-N)

dN/dt = k (6100000 - N)

Step-by-step explanation:

Since, the number N of those people who have heard a certain rumor is proportional to the number of those who have not yet heard the rumor.

The rate of change of number of those who have heard the rumour is = dN/dt

dN/dt = k (P-N)

dN/dt = k (6100000 - N)

Where P is the population of the city = P = 6100000

k is the proportionality constant.

(P-N) = number of those that have not heard the rumour