EVALUATE EXPONENTIAL FUNCTIONS

About "Evaluate exponential functions"

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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ALGEBRA

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