Math Puzzle - Zombies!!!

The video presents a unique math puzzle involving a war between 500 humans and 500 zombies. It sets up differential equations to model the dynamics of the war, where humans and zombies die at rates proportional to each other's numbers. The solution involves solving a second-order linear differential equation to find the number of zombies over time. Initial conditions are used to determine constants, and the outcome shows that zombies win with 516 remaining. The video concludes with a simulation of different scenarios, demonstrating how varying initial conditions affect the outcome.

What is the initial number of humans and zombies in the problem?

• 400 humans and 600 zombies

• 500 humans and 500 zombies

• 600 humans and 400 zombies

• 300 humans and 700 zombies

What is the differential equation for the rate of change of zombies?

• DZ/DT = 4Z - 2H

• DZ/DT = 2Z - 4H

• DZ/DT = 3Z - 5H

• DZ/DT = 5Z - 3H

What is the characteristic equation derived from the differential equation for zombies?

• Lambda^2 + 3Lambda + 15 = 0

• Lambda^2 - 3Lambda - 15 = 0

• Lambda^2 + 5Lambda - 10 = 0

• Lambda^2 - 5Lambda + 10 = 0

What is the expression for the number of zombies over time?

• Z = 60e^(4T) + 440e^(-4T)

• Z = 39.3e^(5.65T) + 460.67e^(-2.65T)

• Z = 50e^(3T) + 450e^(-3T)

• Z = 100e^(2T) + 400e^(-2T)

At what time do humans become extinct in the war?

• T = 0.5

• T = 1.5

• T = 0.837

• T = 1.2

How many zombies remain when humans lose the war?

• 500

• 540

• 516

• 530

What happens if there are 200 fewer zombies initially?

• Both sides are wiped out

• Zombies win

• Humans win

• The war is a draw