Question

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

and f(3) = 16

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)`