The rate at which a rumor spreads in a town is proportional to the product of the number of people who have heard it and the number who have not. If the town has $N$ people and $x(t)$ have heard the rumor, which differential equation models the spread?

Question

Accepted Answer

A. $\dfrac{dx}{dt} = kx(N-x)$

Answer

$\dfrac{dx}{dt} = kx(N-x)$

Answer

$\dfrac{dx}{dt} = kx$

Answer

$\dfrac{dx}{dt} = k(N-x)$

Answer

$\dfrac{dx}{dt} = kx^2$

The rate at which a rumor spreads in a town is proportional to the product of the number of people who have heard it and the number who have not. If the town has $N$ people and $x(t)$ have heard the rumor, which differential equation models the spread?

Explanation

Core Concept

Correct Answer

More Unit 7: Differential Equations practice questions

The rate at which a rumor spreads in a town is proportional to the product of the number of people who have heard it and the number who have not. If the town has NNN people and x(t)x(t)x(t) have heard the rumor, which differential equation models the spread?

Explanation

Core Concept

Correct Answer

More Unit 7: Differential Equations practice questions

The rate at which a rumor spreads in a town is proportional to the product of the number of people who have heard it and the number who have not. If the town has $N$ people and $x(t)$ have heard the rumor, which differential equation models the spread?