Question

Give three real-life examples of applications of exponential or logarithmic functions and give some background information into why these topics are important.

Answer 1

Exponential and logarithmic functions are applied in various real-life scenarios like calculating compound interest, modelling exponential population growth, and measuring the magnitude of earthquakes using the Richter scale. These concepts are vital in fields like science, finance, and engineering.

Step-by-step explanation:

Exponential and logarithmic functions have significant applications in real life. Here are three concrete examples:

1. Compound Interest in finance: The formula for compound interest is an example of an exponential function. It takes the form A = P(1+r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is number of times that interest is compounded per unit t.
2. Population Growth: Exponential functions are often used in models for population growth, particularly for species where the birth rate per individual is constant. The equation for population growth is normally written as N = N0e^(rt), where N is the final population size, N0 is the initial population, e is the base of the natural logarithm, r is the rate of growth, and t is time.
4. Richter Scale: The Richter scale measures the magnitude of an earthquake on a logarithmic scale. Each unit increase in magnitude represents a tenfold increase in measured amplitude and approximately 31.6 times more energy release.

Understanding these topics is important because exponential and logarithmic functions arise in many fields, such as science, finance, and engineering, where variables exhibit exponential growth or decay.

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