Question

1. Find an algebraic representation for an exponential function if it is known that f(x + 1) = 4.f(x)

Answer 1

$f(x)=4^{x-1}$ is the algebraic representation for an exponential function

Step-by-step explanation:

Given:

f(x + 1) = 4.f(x)

f(3) = 16

To Find:

Algebraic representation for an exponential function=?

Solution:

From the formula f(x+n) = $4^n$ f(x)

when n= 1, x= 3

f(3+1)= 4(1)f(3)

f(4)= 4f(3)

Substituting the value of f(3)

f(4)= 4f(3)

f(4)= 4 x 16  

f(4)= 64

f(4)=$4^2$

f (5) = $4^2$ x 16

f (5) = $4^2$ x  $4^2$

f(5)= $4^4$

Similarly,

F(6) = $4^5$

Hence, $f(x)=4^{x-1}$