We're given the following function:
![f(x)=log(.75^x)=log[ (\frac{3}{4}) ^{x}]=log( \frac{3^x}{4^x})](https://tex.z-dn.net/?f=f%28x%29%3Dlog%28.75%5Ex%29%3Dlog%5B%20%20%28%5Cfrac%7B3%7D%7B4%7D%29%20%5E%7Bx%7D%5D%3Dlog%28%20%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%20%20)
In order to see if the function is decreasing we'll take its derivative. If

the function is increasing, if

the function is decreasing.
We take the derivate:
![\frac{d}{dx}[log( \frac{3^x}{4^x})]= \frac{4^x}{3^x}[ \frac{d}{dx} (\frac{3^x}{4^x})]=\frac{4^x}{3^x} \frac{4^x[ \frac{d}{dx} (3^x)]-3^x[ \frac{d}{dx} (4^x)]}{ 4^2^x}=](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5Blog%28%20%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%5D%3D%20%5Cfrac%7B4%5Ex%7D%7B3%5Ex%7D%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%28%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%5D%3D%5Cfrac%7B4%5Ex%7D%7B3%5Ex%7D%20%5Cfrac%7B4%5Ex%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%283%5Ex%29%5D-3%5Ex%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%284%5Ex%29%5D%7D%7B%204%5E2%5Ex%7D%3D)
Which implies the function is decreasing.
Another way to answer the problem (although less insightful) you can take any two real numbers

and

such that

, then if

the function is increasing and if

the function is decreasing. You can verify the function is decreasing with any two numbers in the function's domain.
Answer:
y=-x-3
Step-by-step explanation:
Answer:
Translation 6 units left and 3 units down
Step-by-step explanation:
Each chef receives <span>16.83 pounds of cheese.</span>
Answer:
the percentage is 12%
Step-by-step explanation:
Given that
The 12 students picked up the vanilla cupcake
And, 88 students picked up the chocolate cupcake
We need to find out the percentage of the students picked up a vanilla cupcake
So, the percenatge is
= (12) ÷ (12 + 88) × 100
= 12 ÷ 100 × 100
= 12%
Hence, the percentage is 12%