Underestimating the Exponential Growth Model?
By: Ms. Priyanka Rawat
Tags: Exponential Growth, Bias, Multidisciplinary, Finance

“This articles is a quick go-through of the simple mathematical model of exponential growth . We will also see how bias associated with it affects us in different contexts”

Lets assume you are offered a deal in which your money is tripled every third day. If you invest just Rs. 10 today, how many days will it take you to become a billionaire? Would it be six months? 100 days?

The correct answers is 71 days. If your estimate was way off, its fine as most of the people will underestimate the rate at which value increases. Our tendency to overlook the power of exponential growth has existed for millennia. Even higher level of education does not prevent people from falling into this bias. Lets discuss this model and its biases from different perspectives:

Finance

Most of us are familiar with the compounding effect, where the accrued interest is added in the principle amount, to calculate the interest for next period. Further, if we are considering the scenario of continuous compounding, it merely melts down to being an exponential function as shown below:

People fail to estimate the power of compounding as they choose to rely on intuition (which linearizes the trend) rather than deliberate analysis failing to capture benefits of investing early. Further, one can relate that such bias also causes piling up of unfavorable loans over time.

Biology

In the time of the Sars-CoV-2 virus, scientists, academicians, and practitioners around the world are tirelessly working to achieve a common goal, i.e. to understand the virus and develop its vaccine. From the start, this virus from Wuhan city of China has been surrounded by many conspiracy theories. Although its origin may remain a mystery to most of us, its short term and long term impact on the human lifestyle and the global economy is alarming and quite evident. The World Health Organization after assessing the novel virus had characterized it as a Pandemic on 11th March 2020. Amid all the information, data scientists are on the frontline to draw insights from the global surveillance data on the spread of infection. Many popular data science communities have posted contests to utilize the power of data to know about the behavior of the virus under multiple conditions and variables. The most simple mathematical model to study the spread of the virus is none other than exponential growth model.

It is due to this exponential rate, scientist around the world had demanded a rapid lockdown in early stages. However, for people, widely underestimating the rate of virus spread, had made them less likely to comply with the official advice and rather made them confused about the need for social distancing practices.

Population Growth

The population of a region increases with a certain rate, similar to compound interest calculations, we can derived at the formula for calculating the expected population at a future date. Common man underestimates this growth and hence, lacks the understanding of need for population control.

Nuclear Fission

We had studied in our school that nuclear fission occurs when nucleus of an atom divides into two nuclei. This may be spontaneous or explicitly done by bombardment of neutrons. In nuclear energy plants, Uranium-235 isotope is excited (by neutrons) which causes splitting of its nucleus into nuclei with further release of neutrons (as nuclear ratio is higher for higher atomic number elements). If Uranium atoms are arranged such that neutrons released from one fission results in more nuclei fission, then a chain reaction occurs that is again exponential in nature. To prevent the outcome of an atomic bomb (which happens when exponential nature of nuclear fission is given a freehand), the nuclear reactors are designed to control the splitting of nuclei by reducing the number of neutrons emitted during the fission process.

References:

David Robson, “Exponential growth bias: The numerical error behind Covid-19” (13th August 2020)