Question

the rate by which people are infected by the zombie plague is proportional to the number of people already infected. let x denote the number of people infected. What is the differential equation describing the number of people infected? Denote the proportionality constant by k. What are the units for k in the differential equation?What is the general solution to this equation?What are the units for k in the solution?

Answer 1

The differential equation describing the number of people infected by the zombie plague is dX/dt = kX, where X represents the number of infected people and k is the proportionality constant. The units for k in the differential equation are people per time. The general solution to this equation is X(t) = Ce^(kt), where e is the base of the natural logarithm. The units for k in the solution are 1/time.

Step-by-step explanation:

The differential equation describing the number of people infected by the zombie plague is dX/dt = kX, where X represents the number of infected people and k is the proportionality constant. The units for k in the differential equation are people per time.

To find the general solution to this equation, we can separate the variables and integrate both sides: 1/X dX = k dt. Integrating, we get ln|X| = kt + C where C is the constant of integration.

The general solution is X(t) = Ce^(kt), where e is the base of the natural logarithm. The units for k in the solution are 1/time.