SECTION 10.4: Exponential Growth and Decay

A solution is defined as a function that is the same as its derivative. For example, an exponential function of the form e^x has a derivative equal to e^x. For an exponential equation, if the function contains a constant (k), the derivative of the function is a constant times the function, i.e., essentially the same as the original function. It implies that the rate of change of e^x is proportional to e^x where the constant k is the constant of proportionality.

The general equation for an exponential function is y = C(e^kt) where k is defines exponential growth if more than 0 and exponential decay if less than 0. The constant C is the value of y when t is 0. In a growth function expressing population, C would represent the initial population.

Exponential growth and decay can occur in many every day circumstances. It is relevant in the study of population growth, marine biology, pollution in cities, drug levels in people etc. My intended major still stands to be economics and so i am definitely aware through the book and other instances that learning to understand rates of change of derivatives functions whether those of exponential growth or decay are important to understand many aspects of banking (beyond just compund interest).