Usually, a virus or bacteria are contagious, which means that they can be spread from person to person. If one person contracts the disease at that point, this person may infect two others. Those two people can potentially infect four more, and this goes on, depending on how contagious a disease is.
In the case of Covid 19, the number of infected people can be doubled or even tripled within a few days. When drawing a graph, the numbers look like a curved line to the right, which gets sharper. This feature is called the exponential spread.
When Covid 19 started around the world, at first in the United States the numbers of cases were very low. From Jan to March 2020, the numbers of infected people with the new virus were few hundreds. From March to April we can see a jump in the numbers up to 1. 7million people. Four months later, in Aug, this number reaches 6.4 million. By the end of the year, in Dec 2020 the number of people infected by Coronavirus hits 19.2 million. By looking at the graph, the exponential equation for the population of infected people in the United States can be calculated as f(x)= (1.285)x-1, where x is based on the month starting from Jan 2020 and f(x) is the number of infected people in million.
If the vaccination has not been started we could anticipate that in June 2021, 18 months later, the number of infected people would pass 90.25 million.
I calculated this formula by looking at sample numbers of (4, 1.7), (8, 6.4), and (12, 19.2). This graph and the numbers are ascending. We know that the general formula for an exponential equation is f(x) = a+bx. Since our initial value is (0.0) (assuming that the numbers of infected people in Jan 2020 are so low that is close to 0), so, a=-1. I found the value of b by the proportion of the increase in the value of f(x). Knowing these values helped me to calculate the exponential formula for something that I deal with on a daily basis these days, the number of infected people by the Covid 19 virus!
P.S: The numbers have been rounded for simplicity.