![]() ![]() Exponential growth refers to an increase based on a constant multiplicative rate of change over equal increments of time, that is, a percent increase of the original amount over time.Percent change refers to a change based on a percent of the original amount.Are these words used correctly? The words certainly appear frequently in the media. What exactly does it mean to grow exponentially? What does the word double have in common with percent increase? People toss these words around errantly. If this rate continues, vegans will make up 10% of the U.S. ![]() In 2011, 2.5% of the population was vegan, adhering to a diet that does not include any animal products-no meat, poultry, fish, dairy, or eggs. ![]() Defining an Exponential FunctionĪ study found that the percent of the population who are vegans in the United States doubled from 2009 to 2011. The scenario in the India population example is different because we have a percent change per unit time (rather than a constant change) in the number of people. For example, in the equation f ( x ) = 3 x + 4, f ( x ) = 3 x + 4, the slope tells us the output increases by 3 each time the input increases by 1. When exploring linear growth, we observed a constant rate of change-a constant number by which the output increased for each unit increase in input. In this section, we will take a look at exponential functions, which model this kind of rapid growth. To a mathematician, however, the term exponential growth has a very specific meaning. When populations grow rapidly, we often say that the growth is “exponential,” meaning that something is growing very rapidly. If this rate continues, the population of India will exceed China’s population by the year 2031. The population is growing at a rate of about 1.2 % 1.2 % each year 2. India is the second most populous country in the world with a population of about 1.25 1.25 billion people in 2013. Evaluate exponential functions with base e e.Find the equation of an exponential function. ![]()
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