Mathematics : Basic Algebra

**Exponents and
Radicals**

First we shall consider exponents.

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**1. Exponents**

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**2. Radicals**

**Question:**

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**3. Exponential
Function**

**Properties of
Exponential Function**

**A Special
Exponential Function**

Among all exponential
functions, *f*(*x*) = *e*^{x}, x *∈* R is the most important one as it has
applications in many areas like mathematics, science and economics. Then what
is this *e*? The following illustration from compounding interest problem
leads to the constant *e.*

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**Illustration**

**Compound
Interest**

We notice that as *n* gets really large, *A*_{n} values seem to be
getting closer to 2.718281815..... Actually *A*_{n} values approach a real
number* e, *an irrational number. 2.718281815 is an approximation to* e*. So* *the compound interest
formula becomes *A* = *P e*^{rt}, where *r* is the interest rate and *P* is the principal and *t* is the number of years. This is called Continuous Compounding.

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11th Mathematics : UNIT 2 : Basic Algebra : Exponents and Radicals | Definition, Formula, Solved Example Problems, Exercise | Mathematics