This study explores the practical applications of exponential functions, particularly the Euler number e, in real-life scenarios. The report emphasizes the use of exponential functions in various fields such as economics, physics, and engineering. It discusses the real value of money, Bitcoin value, household savings, factory production, and forest exploitation. The study also examines the consequences of these problems and provides solutions. The Euler number e is derived from compound interest and is approximately 2.71828. It is the base of the natural logarithm and is crucial in solving differential equations. The exponential function e^x has the unique property that its derivative is itself, making it essential in modeling natural phenomena. The study also discusses input-output analysis, which is used to examine economic dynamics, risk pricing in global markets, and non-linear systems. It highlights the importance of input-output analysis in understanding complex systems and informing economic policies. The real value of money is calculated using exponential functions to account for inflation. For example, a person who invests 500,000 rupees in a fixed deposit for five years will see an increase in the value of their investment, adjusted for inflation. The study shows that the actual surplus from the investment is higher than the nominal increase due to inflation. The study also examines the growth of production in a manufacturing company, showing how exponential functions can be used to predict future production levels. It calculates the time required for a company to produce 10,000 units, given a 5% annual increase in production. The value of Bitcoin is also analyzed using exponential functions, showing how its value can increase exponentially over time. Similarly, the study examines deforestation rates, showing how exponential functions can be used to model the increasing number of trees cut down over time. Finally, the study uses geometric series to calculate the total savings of a person who saves money in a pattern of doubling each month. The total savings after 10 months is calculated using the formula for the sum of a geometric series.This study explores the practical applications of exponential functions, particularly the Euler number e, in real-life scenarios. The report emphasizes the use of exponential functions in various fields such as economics, physics, and engineering. It discusses the real value of money, Bitcoin value, household savings, factory production, and forest exploitation. The study also examines the consequences of these problems and provides solutions. The Euler number e is derived from compound interest and is approximately 2.71828. It is the base of the natural logarithm and is crucial in solving differential equations. The exponential function e^x has the unique property that its derivative is itself, making it essential in modeling natural phenomena. The study also discusses input-output analysis, which is used to examine economic dynamics, risk pricing in global markets, and non-linear systems. It highlights the importance of input-output analysis in understanding complex systems and informing economic policies. The real value of money is calculated using exponential functions to account for inflation. For example, a person who invests 500,000 rupees in a fixed deposit for five years will see an increase in the value of their investment, adjusted for inflation. The study shows that the actual surplus from the investment is higher than the nominal increase due to inflation. The study also examines the growth of production in a manufacturing company, showing how exponential functions can be used to predict future production levels. It calculates the time required for a company to produce 10,000 units, given a 5% annual increase in production. The value of Bitcoin is also analyzed using exponential functions, showing how its value can increase exponentially over time. Similarly, the study examines deforestation rates, showing how exponential functions can be used to model the increasing number of trees cut down over time. Finally, the study uses geometric series to calculate the total savings of a person who saves money in a pattern of doubling each month. The total savings after 10 months is calculated using the formula for the sum of a geometric series.