Answer:
[tex]f(x) = -12(\frac{1}{4})^x[/tex]
Step-by-step explanation:
Given function,
[tex]f(x)=-3\times 4^{1-x}[/tex]
Using the product rule of exponent i.e. [tex]a^m.a^n=a^{m+n}[/tex]
[tex]f(x) = -3 \times 4 \times 4^{-x}[/tex]
[tex]f(x) = -12\times 4^{-x}[/tex]
Using power of power rule of exponent i.e. [tex](a^b)^c = a^{bc}[/tex]
[tex]f(x) = -12(4^{-1})^x[/tex]
Since, [tex]a^m =\frac{1}{a^{-m}}[/tex]
[tex]\implies f(x) = -12(\frac{1}{4})^x[/tex]
Which is the required form of [tex]f(x) = ab^x[/tex]
Where,
a = -12, b = 1/4
