Answer:
[tex]\displaystyle f(x)=-\frac{1}{16}(4^x)[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=-4^{x-2}[/tex]
And we want to convert this to the exponential form:
[tex]f(x)=ab^x[/tex]
First, using the power of a product property, we can rewrite our function as:
[tex]f(x)=-(4^x\cdot4^{-2})[/tex]
By evaluating the second term, we acquire:
[tex]\displaystyle f(x)=-\big(4^x\cdot \frac{1}{4}^2}\big)=-\big(4^x\cdot \frac{1}{16}\big)[/tex]
So, by rearranging, we acquire:
[tex]\displaystyle f(x)=-\frac{1}{16}(4^x)[/tex]
As desired.
