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Algebra for Athletes.com

How It’s Used

The material mechanics that we’ve learned are a basic part of all mechanical and structural design. Architects,  structural engineers,  civil engineers,  and mechanical engineers do this with nearly everything they design.  Exponents also appear in other fields as well.   Just about every field that studies growth uses exponents.

One example is the growth of money in a savings account.   The amount of money in the account grows as interest is added.   The basic formula for earning interest is:

 where:          F = the Future amount after all of the interest is added

P = the Present value of the money when it starts gaining interest

i = the interest rate per compounding period

n = the number of compounding periods 

A compounding period is how often the interest is added. For example, if your account has annual interest rate of 5% compounded weekly, then every week 0.05/52 x the amount in the account is added (52 weeks per year). If the account has an annual rate of 5% compounded daily, then 0.05/365 x the amount is added. So the more frequently the money is compounded, the faster it will grow. If you put $1,000 in a savings account with an interest rate of 4% compounded daily, the amount at the end of a year would be: 

The branch of math called logarithms studies exponential growth and exponential decay. Exponential growth is studied in biology. If a group of animals enters a new habitat, its population will grow exponentially if they have unlimited food and limited predators.

Exponents are also used to study decay. Radioactive materials like plutonium decay exponentially over time. As they decay, they become less harmful. Exponents are used to determine how long it will take radioactive waste from nuclear power plants to decay to a point where they'll no longer create health risks like causing cancer. 

Exponential decay of radioactive materials has another important use in science. A particular form of the element carbon, C¹⁴ (carbon 14), decays exponentially into the more common form of carbon, C¹² (carbon 12). Since the amount of C¹⁴ remains relatively constant in the atmosphere, the amount of C¹⁴ in plants and animals that absorb it stays relatively constant. When the plant or animal dies and stops absorbing C¹⁴, the C¹⁴ begins to decay. If you find a fossil of the plant or animal, you can measure the amounts of C¹⁴ and other forms of carbon in it. By comparing the amount of C¹⁴ with the other forms of carbon, you can determine how much C¹⁴ has decayed. Since scientists have determined the rate of decay of C¹⁴ , you can tell how long the C¹⁴ in the fossil has been decaying. In other words, you can tell how old the fossil is. This is how scientists determine the age of fossils and archeological artifacts.