**Evaluate exponential functions :**

To evaluate exponential functions, we have to apply the given value of x in the given question and simplify.

In mathematics, an exponential function is a function of the form. in which the input variable x occurs as an exponent.

Before going to see example problems, we must know the basic rules in exponents.

- The exponents of a number says how many times to use the number in a multiplication. For example 5³ = 5 x 5 x 5
- If we have negative exponent in the question, first we have to convert the negative exponent as positive then apply the given value of x and evaluate.

Let us see some examples

**Example 1 :**

Evaluate the following exponential function at the given value

**Solution :**

**Evaluate the following exponential function at the given value **

**Example 2 :**

Evaluate the following exponential function at the given value

f(n) = 10 x 2^n

Here the value of n is 5.So we are going to apply 5 instead of the variable n.

f(5) = 10 x 2^5

= 10 x (2 x 2 x 2 x 2 x 2) (Repeating 2 five times)

= 10 x 32

= 320

Hence the answer is 320.

**Example 3 :**

Evaluate the following exponential function at the given value

f(n) = 10 x 2^n

Here the value of n is -2.So we are going to apply -2 instead of the variable n.

f(-2) = 10 x 2^(-2)

Since we have negative power, first we have to make it as positive then apply the value and simplify.

= 10 (1/2^2)

= 10 x (1/2 x 2)

= 10/4

= 5/2

Hence the answer is 5/2.

**Example 4 :**

Evaluate the following exponential function at the given value

g(x) = (1/5) x (1/3)^x

Here the value of x is 3.So we are going to apply 3 instead of the variable x.

g(3) = (1/5) x (1/3)^3

= (1/5) x (1/3)^3 (Repeating 1/3 three times)

= (1/5) x (1/3) x (1/3) x (1/3)

= (1/5) x (1/27)

= 1/135

Hence the answer is 1/135.

**Example 5 :**

Evaluate the following exponential function at the given value

f(x) = (1/2) x (3)^x

Here the value of x is 4.So we are going to apply 4 instead of the variable x.

f(x) = (1/2) x (3)^4

= (1/2) x (3)^4 (Repeating 3 four times)

= (1/2) x (3 x 3 x 3 x 3)

= (1/5) x (81)

= 81/5

Hence the answer is 81/5.

After having gone through the stuff given above, we hope that the students would have understood "Evaluate exponential functions".

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