EVALUATE EXPONENTIAL FUNCTIONS

To evaluate an exponential function with the form

f(x)  =  b^x,

we simply substitute x with the given value, and calculate the resulting power.  

Example 1 : 

Evaluate :

f(x)  =  (1/3) ⋅ 6^x at x = 2

Solution : 

f(x)  =  (1/3) ⋅ 6^x

Substitute 2 for x. 

f(2)  =  (1/3) ⋅ 6²

=  (1/3) ⋅ 36

=  12

Example 2 : 

Evaluate :

f(n)  =  10 ⋅ 2ⁿ at n = 5

Solution : 

f(n)  =  10 ⋅ 2ⁿ

Substitute 5 for n. 

f(5)  =  10 ⋅ 2⁵

=  10 ⋅ 32

=  320

Example 3 : 

Evaluate :

f(n)  =  8 ⋅ 2ⁿ at n = -2

Solution : 

f(n)  =  8 ⋅ 2ⁿ

Substitute -2 for n. 

f(-2)  =  8 ⋅ 2^-2

=  8 ⋅ 1/2²

=  8 ⋅ 1/4

=  2

Example 4 : 

Evaluate :

g(x)  =  (1/5) ⋅ (1/3)^x at x = 3

Solution : 

g(x)  =  (1/5) ⋅ (1/3)^x

Substitute 3 for x. 

g(3)  =  (1/5) ⋅ (1/3)³

Power of a Quotient Property. 

=  (1/5) ⋅ (1³/3³)

=  (1/5) ⋅ (1/27)

=  1/135

Example 5 : 

Evaluate :

g(x)  =  (1/121) ⋅ 3^x at x = 4

Solution : 

g(x)  =  (1/121) ⋅ 3^x

Substitute 4 for x. 

g(4)  =  (1/121) ⋅ 3⁴

Power of a Quotient Property. 

=  (1/121) ⋅ 81

=  81/135

Example 6 : 

Biologists use a formula to estimate the mass of a mammal's brain. For a mammal with a mass of m grams, the approximate mass B of the brain, also in grams, is given by B = (1/8)m^2/3. Find the approximate mass of the brain of a mouse that has a mass of 64 grams.   

Solution : 

B  =  (1/8)m^2/3

Substitute 64 for m. 

=  (1/8)(64)^2/3

=  (1/8)(4³)^2/3

Power of a Power Property. 

=  (1/8)(4^3 ⋅ 2/3)

=  (1/8)(4²)

=  (1/8)(16)

=  2

The approximate mass of the brain of the mouse is 2 grams. 

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.