Answer:
![\frac{1}{2} x - 4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20x%20-%204)
Step-by-step explanation:
Perpendicular lines will have slopes that are the multiplicative additive inverse of each other: a line with slope 3/4 is perpendicular to a line with slope -4/3, for example. You need a line that is perpendicular to a line with slope -2 (reading that from the -2 in the -2x portion of the given equation, which is written in slope-intercept form), so your new line must have slope +1/2.
With the slope and a point, we can come up with an equation using this formula:
y - y-coordinate = slope (x - x-coordinate)
So we have y - (-2) = 1/2 (x - 4).
Simplify the equation: y + 2 = 1/2 x - 2
Subtract 2 from both sides: y + 2 - 2 = 1/2 x - 2 - 2
Simplify: y = 1/2 x - 4.
Answer:8,5 recirpoal is 5,8
Step-by-step explanation:
The general formula for exponential growth and decays is:
![y=y_0e^{kx}](https://tex.z-dn.net/?f=y%3Dy_0e%5E%7Bkx%7D)
if k>0 then then it is an exponential growth function. If k<0 then the function represents an exponential decay.
Now we need to classify each of the functions:
1.
The function
![y=\frac{1}{4}(\frac{1}{e})^{-2x}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B4%7D%28%5Cfrac%7B1%7D%7Be%7D%29%5E%7B-2x%7D)
can be wrtten as:
![\begin{gathered} y=\frac{1}{4}(e^{-1})^{-2x}^{} \\ =\frac{1}{4}e^{2x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%5Cfrac%7B1%7D%7B4%7D%28e%5E%7B-1%7D%29%5E%7B-2x%7D%5E%7B%7D%20%5C%5C%20%3D%5Cfrac%7B1%7D%7B4%7De%5E%7B2x%7D%20%5Cend%7Bgathered%7D)
comparing with the general formula we notice that k=2, therefore this is an exponential growth.
2.
The function
![y=(\frac{1}{e})^{4x}](https://tex.z-dn.net/?f=y%3D%28%5Cfrac%7B1%7D%7Be%7D%29%5E%7B4x%7D)
can be written as:
![\begin{gathered} y=(\frac{1}{e})^{4x} \\ y=(e^{-1})^{4x} \\ y=e^{-4x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%28%5Cfrac%7B1%7D%7Be%7D%29%5E%7B4x%7D%20%5C%5C%20y%3D%28e%5E%7B-1%7D%29%5E%7B4x%7D%20%5C%5C%20y%3De%5E%7B-4x%7D%20%5Cend%7Bgathered%7D)
comparing with the general formula we notice that k=-4, therefore this is an exponential decay.
3.
The function
![y=2e^{-x}+1](https://tex.z-dn.net/?f=y%3D2e%5E%7B-x%7D%2B1)
comparing with the general formula we notice that k=-1, therefore this is an exponential decay.
Answer:
y = 3x - 7
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
2x5.4x4.5x4.2x5.3x3. 5.5x3