Question

We can find math in everyday life.Explain how exponential functions are related to real life.In your explanation, give an example of a real life situation.

Real Subject is: Algebra 1

Answer 1

Exponential functions model situations with growth or decay in real life, such as population growth and compound interest. They describe how values change proportionally over time and are essential for understanding various real-world phenomena.

Step-by-step explanation:

Exponential functions are related to real life as they describe situations where growth or decay is proportional to the current value. For instance, population growth can often be modeled using an exponential function. If a population of bacteria starts with 10 cells and doubles every hour, the number of bacteria after t hours is given by the function P(t) = 10 × 2t. Here, the base number (2) is expressed as eln(2) to tie into the properties of natural logarithms and exponentials.

Another real-life example of exponential growth is compound interest in finance. When money earns interest at a certain rate that is compounded annually, the amount of money grows exponentially. The formula for compound interest A = P(1 + r/n)nt, represents the amount A after t years, starting with principal amount P, at an annual interest rate r, compounded n times per year.

The use of logarithms and exponential numbers help us to calculate growth rates, half-lives in biology or chemistry, and many other phenomena in economics and engineering.

Answer 2

We use it in everyday life to do things such as Money or Population. Like your pay could go up or the population somewhere can increase to a point where the country or town has to raise prices or lower them, and get more of something.

Example:

You have someone babysit for you and you give them $15 a hour. They do a lot less work then you expected and spent most of the time looking at there phone. You might lower the pay due to them most the time just playing on there phone.