[tex]f(x)=4^{x-1}[/tex] 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) = [tex]4^n[/tex] 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)=[tex]4^2[/tex]
f (5) = [tex]4^2[/tex] x 16
f (5) = [tex]4^2[/tex] x [tex]4^2[/tex]
f(5)= [tex]4^4[/tex]
Similarly,
F(6) = [tex]4^5[/tex]
Hence, [tex]f(x)=4^{x-1}[/tex]
