Question

Write the exponential function f(x)=-3*4^(1-x) in the form f(x)=ab^x

Answer 1

Answer:

$f(x) = -12(\frac{1}{4})^x$

Step-by-step explanation:

Given function,

$f(x)=-3\times 4^{1-x}$

Using the product rule of exponent i.e. $a^m.a^n=a^{m+n}$

$f(x) = -3 \times 4 \times 4^{-x}$

$f(x) = -12\times 4^{-x}$

Using power of power rule of exponent i.e. $(a^b)^c = a^{bc}$

$f(x) = -12(4^{-1})^x$

Since, $a^m =\frac{1}{a^{-m}}$

$\implies f(x) = -12(\frac{1}{4})^x$

Which is the required form of $f(x) = ab^x$

Where,

a = -12, b = 1/4

Answer 2

f(x)=-3*4^(1-x)

= -3 * 4^1 * 4^(-x)

= -12 4^(-x)

= -12 (1/4)^x