Answer:
Last Graph (4th one)
Step-by-step explanation:
The equation given is ![A(x)=400*b^x + 0\\A(x) = 400b^x](https://tex.z-dn.net/?f=A%28x%29%3D400%2Ab%5Ex%20%2B%200%5C%5CA%28x%29%20%3D%20400b%5Ex)
Since we want increase of 25%, the value of b would be 1.25, so we have:
![A(x)=400(1.25)^x](https://tex.z-dn.net/?f=A%28x%29%3D400%281.25%29%5Ex)
The graph should be increasing so we can immediately eliminate 2nd and 3rd graphs since they are clearly decreasing. We now have to choose between 1st graph and 4th graph.
<u>1st graph:</u>
Let's take the point (-20,30)
![A(x)=400(1.25)^{-20}\\A(x)=4.65](https://tex.z-dn.net/?f=A%28x%29%3D400%281.25%29%5E%7B-20%7D%5C%5CA%28x%29%3D4.65)
<u>2nd graph:</u>
Let's take the point (-20,4.5)
![A(x)=400(1.25)^{-20}\\A(x)=4.65](https://tex.z-dn.net/?f=A%28x%29%3D400%281.25%29%5E%7B-20%7D%5C%5CA%28x%29%3D4.65)
hence, this makes sense. So the correct graph is 4th one.
.00000000058 because the exponent is negative the decimal goes backwards 10 times
We are given the equation:
![x+\frac{1}{6}=\frac{-2}{3}](https://tex.z-dn.net/?f=x%2B%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B-2%7D%7B3%7D)
Now we have fraction 1/6 in addition on the left side.
So we apply opposite operation of addition on the right side.
Subtracting 1/6 from right side we have,
![x=\frac{-2}{3}-\frac{1}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%7D%7B3%7D-%5Cfrac%7B1%7D%7B6%7D)
Now in fraction addition and subtraction , we have to find the lcd first.
LCD of 3 and 6 is 6,
![x=\frac{-4}{6}-\frac{1}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4%7D%7B6%7D-%5Cfrac%7B1%7D%7B6%7D)
x=-5/6
Answer: x=-5/6