Answer:
![f(x)=5120(1.25)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D5120%281.25%29%5E%7Bx%7D)
Step-by-step explanation:
As per the given question
As we know that
f(x) and x are related by following equation
![f(x)=a( {b})^{x}](https://tex.z-dn.net/?f=f%28x%29%3Da%28%20%7Bb%7D%29%5E%7Bx%7D)
where
b is the common ratio
Now first we have to compute the value for b which are as follows
![\frac{6400}{5120}= 1.25](https://tex.z-dn.net/?f=%5Cfrac%7B6400%7D%7B5120%7D%3D%201.25)
![\frac{8000}{6400}= 1.25](https://tex.z-dn.net/?f=%5Cfrac%7B8000%7D%7B6400%7D%3D%201.25)
Like if we take the ratio by this method than it comes 1.25
Therefore the common ratio, b = 1.25
So,
a = 5,120
Hence, the equation which model the relationship between the number of weeks and the number of viewers is
![f(x)=5120(1.25)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D5120%281.25%29%5E%7Bx%7D)
Answer:
Step-by-step explanation:
When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.
It is given by:
![$ (y - y_1) = m (x - x_1) $](https://tex.z-dn.net/?f=%24%20%28y%20-%20y_1%29%20%3D%20m%20%28x%20-%20x_1%29%20%24)
where
is the slope of the line and
is the point passing through it.
Here,
and ![$ (x_1,y_1) = (-4,8) $](https://tex.z-dn.net/?f=%24%20%28x_1%2Cy_1%29%20%3D%20%28-4%2C8%29%20%24)
Substituting in the equation:
![$ y - 8 = \frac{-1}{4} (x + 4) $](https://tex.z-dn.net/?f=%24%20y%20-%208%20%3D%20%5Cfrac%7B-1%7D%7B4%7D%20%28x%20%2B%204%29%20%24)
![$ \implies 4y - 32 = -x - 4 $](https://tex.z-dn.net/?f=%24%20%5Cimplies%204y%20-%2032%20%3D%20-x%20-%204%20%24)
![$ \implies x + 4y - 28 = 0 $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20x%20%2B%204y%20-%2028%20%3D%200%20%24)
Hun, nothing is attatched. Try to attach something or tell me the problem? I'll try and answer it..
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The general formula for a equation of the form:
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
is:
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
In this case we notice that a=1, b=-4 and c=3. Plugging this values in the general formula we get:
![\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(3)}}{2(1)} \\ =\frac{4\pm\sqrt[]{16-12}}{2} \\ =\frac{4\pm\sqrt[]{4}}{2} \\ =\frac{4\pm2}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D%5Cfrac%7B-%28-4%29%5Cpm%5Csqrt%5B%5D%7B%28-4%29%5E2-4%281%29%283%29%7D%7D%7B2%281%29%7D%20%5C%5C%20%3D%5Cfrac%7B4%5Cpm%5Csqrt%5B%5D%7B16-12%7D%7D%7B2%7D%20%5C%5C%20%3D%5Cfrac%7B4%5Cpm%5Csqrt%5B%5D%7B4%7D%7D%7B2%7D%20%5C%5C%20%3D%5Cfrac%7B4%5Cpm2%7D%7B2%7D%20%5Cend%7Bgathered%7D)
then:
![x_1=\frac{4+2}{2}=\frac{6}{2}=3](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B4%2B2%7D%7B2%7D%3D%5Cfrac%7B6%7D%7B2%7D%3D3)
and
![x_2=\frac{4-2}{2}=\frac{2}{2}=1](https://tex.z-dn.net/?f=x_2%3D%5Cfrac%7B4-2%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B2%7D%3D1)
Therefore, x=3 or x=1.
Answer:
11000
Step-by-step explanation: