## exponential growth

### y = 2ˣ

Exponential growth is a concept in mathematics where a quantity or value increases at an accelerated rate over time. This concept can be observed in many real-life scenarios, such as population growth, compound interest, and the spread of infectious diseases. In an exponential growth scenario, the growth rate is proportional to the current size or value of the quantity. Hence, as the quantity grows, the rate of growth also increases, causing a rapid increase in the value.

For example, let’s consider the population of a city. If the city’s population is growing at an annual rate of 2% and there are currently 100,000 residents, then the population after one year will be 102,000. In the second year, the population will be 104,040, and in the third year, it will be 106,120. As you can see, the population is growing more and more each year, even though the growth rate remains the same.

One important thing to note about exponential growth is that it is unsustainable in the long run. Eventually, the growth rate will begin to slow down as the quantity approaches its maximum limit or capacity. This is known as a saturation point or carrying capacity. In the case of our city population example, the growth rate will begin to slow down as the city runs out of resources, such as housing, food, and jobs. Therefore, it is important to consider the long-term effects of exponential growth and implement strategies to manage it effectively.

##### More Answers:

How To Find The Derivative Of A Function And Use It To Find Slope And Tangent Line EquationFinding X-Intercepts: How To Locate Where A Function Crosses The X-Axis

Exponential Decay: A Mathematical Process For Quantitative Decrease