An interesting perspective is understanding this topic through the spread of viral infections. A virus can begin to spread when there is no known immunization or vaccine for it, and each infected person can infect anyone they come in contact with. Taking this into consideration in terms of the COVID-19 pandemic that began in 2020 and is still ongoing, it is interesting to observe the fluctuations in the growth of the virus as a result of not having the vaccine, and the decay of the spread of the virus after people were beginning to get vaccinated. Exponential growth at the beginning of the pandemic caused the rates of people infected to grow very high. For example, if there were 150 cases reported in Los Angeles County on the first day of the pandemic, and had an increasing infection rate at around 7%, after a week we could assume that there were roughly 241 new cases. This was calculated by multiplying the initial number of cases, by the growth factor, 1.07 to the power of 7, which was the total time spanned. The percentage change can be calculated by subtracting the final number of cases for the week, 241, by the initial number of cases, 150, and dividing by the initial number of cases, which would result in a 60.7% percent change. This is just a small example of what might’ve happened in terms of the growth of the COVID-19 virus. Once the vaccine was introduced, cases began to exponentially decay. For example, the population of infected people in the City of Los Angeles as of now is about 1,500. Each week, the population’s infection rate will decrease by 4%. After 4 weeks or a month, the number of infected people will be 1,274. The decay factor is 0.96, and it is multiplied by the initial population. The growth factor is raised to the exponent of time. The percentage change in cases is calculated again by subtracting the final and an initial number of cases and dividing them by the initial number. The percentage change in cases is 17.7%.

Sources: 

https://www.nytimes.com/2021/04/29/opinion/covid-exponential-decay.html