Technical Math Education

How Fast is Exponential Growth?

What is exponential growth and how does it happen? An example of exponential growth is the rate at which something multiplies in a time period. If two rabbits breed one day and the new born rabbits grow in a few months, the population will double within a few days. If we study population growth, we see that it increases at a speed of r to the power of time. And the weeds in a pond multiply by three each day.

The rate at which the population increases is called the exponential growth rate. In simple terms, the exponential growth rate is the rate at which the population increases by two or morefold in a specified amount of time. For example, if you have one person with an infectious disease in a country of millions, the number of infected individuals will double every three days. By January 31, the number of infected people will have doubled and by March 19, it will have grown to a billion.

Assuming you’re using an example of a hypothetical red kite population, it is important to understand that exponential growth has an upper limit. As the population grows, the area they inhabit will shrink. As the number of cases increase, the number of susceptible individuals will decrease. The rate of a disease’s spread will slow down when it reaches a certain percentage of the population. As the population gets smaller, the disease will become a minor problem.

In the real world, the exponential growth rate is 10%. In other words, the number of infected people will double every three days. On January 31, the number of infected persons will have doubled to twenty. On March 19, the number of infected people will reach two hundred thousand. Then the population will have doubled once again. And so on. So exponential growth happens everywhere. It’s the basis of many inventions and innovations.

If a disease spreads through a person’s body, it is exponential. A single virus will spread through a city’s population in less than three days. And a single infection can become a full-blown pandemic if two people are infected with it. The numbers of infected people will double every three to four days. In the UK, the number of infected people will double in three to four days.

When it comes to the human population, exponential growth is common in many aspects of daily life. For example, the human population grows by approximately two million people every year. Facebook’s user base triples every three to four days. In contrast, the amount of SARS-CoV-2 deaths in the UK doubles each year. By the time the disease is wiped out, the number of cases will double again. The number of people infected with COVID-19 will double in the UK.

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