Question

5. A bacteria population grows in such a way that its growth rate at time t is equal to its population by 5:

5.1. Describe the process by a differential equation​

Answer 1

To describe the process of bacteria population growth as a differential equation, we can use the concept of exponential growth. Let's denote the population of the bacteria at time t as P(t). According to the given information, the growth rate of the population at any given time t is equal to the population itself multiplied by 5.

Mathematically, we can express this as:

dP(t)/dt = 5 * P(t)

Here, dP(t)/dt represents the derivative of the population with respect to time, indicating the rate of change of the population at time t. The equation states that this rate of change is equal to 5 times the population at that time.

This differential equation captures the exponential growth pattern observed in the bacteria population, where the growth rate is directly proportional to the population size. By solving this differential equation, we can determine the specific function P(t) that describes the growth of the bacteria population over time.