Question

A population of bacteria, growing according to the Malthusian model, doubles itself in 10 days. If there are 1000 bacteria present initially, how long will it take the population to reach 10,000 ?

   A population of bacteria, growing according to the Malthusian model, doubles itself in 10 days. If there are 1000 bacteria present initially, how long will it take the population to reach 10,000 ?

Differential Equations with Boundary Value Problems

Differential Equations with Boundary Value Problems

John Polking, Al… 2nd Edition

Chapter 3, Problem 4

Instant Answer

Solved by Expert Khushbu Rani

09/14/2023

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A population of bacteria, growing according to the Malthusian model, doubles itself in 10 days. If there are 1000 bacteria present initially, how long will it take the population to reach 10,000 ?

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Key Concepts

Doubling Time

Doubling time is the period required for a quantity undergoing exponential growth to double in size. It is a key concept in understanding exponential processes, as knowledge of the doubling time allows for easy estimation of the growth over any given period by applying logarithmic relationships.

Exponential Growth

Exponential growth is a process in which the quantity increases by a constant multiplier over equal time increments. It is characterized by a rapidly accelerating increase, commonly modeled using equations involving exponential functions and natural logarithms.

Malthusian Growth Model

The Malthusian growth model describes a population that grows exponentially over time, where the rate of growth is proportional to the current population. This model assumes a constant per capita growth rate, meaning that the population increases by the same percentage in any equal time interval.

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