Answer:
Vaush
Step-by-step explanation:
You can have 30 and a negative 6. IDK. Hope it can help a bit.
The answer is letter B because I guessed but I mean just try it lol
Function transformation involves changing the form of a function
The function g(x) is ![\mathbf{g(x) = 8(2)^x}](https://tex.z-dn.net/?f=%5Cmathbf%7Bg%28x%29%20%3D%208%282%29%5Ex%7D)
The function is given as:
![\mathbf{f(x) = 3^x}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%203%5Ex%7D)
g(x) is an exponential function that passes through points (-2,2) and (-1,4).
An exponential function is represented as:
![\mathbf{y = ab^x}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20ab%5Ex%7D)
At point (-2,2), we have:
![\mathbf{2 = ab^{-2}}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%20%3D%20ab%5E%7B-2%7D%7D)
At point (-1,4), we have:
![\mathbf{4 = ab^{-1}}](https://tex.z-dn.net/?f=%5Cmathbf%7B4%20%3D%20ab%5E%7B-1%7D%7D)
Divide both equations
![\mathbf{\frac 42=\frac{ab^{-1}}{ab^{-2}}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%2042%3D%5Cfrac%7Bab%5E%7B-1%7D%7D%7Bab%5E%7B-2%7D%7D%7D)
Simplify
![\mathbf{2=\frac{b^{-1}}{b^{-2}}}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%3D%5Cfrac%7Bb%5E%7B-1%7D%7D%7Bb%5E%7B-2%7D%7D%7D)
Apply law of indices
![\mathbf{2=b^{-1+2}}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%3Db%5E%7B-1%2B2%7D%7D)
![\mathbf{2=b}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%3Db%7D)
Rewrite as:
![\mathbf{b =2}](https://tex.z-dn.net/?f=%5Cmathbf%7Bb%20%3D2%7D)
Substitute 2 for b in ![\mathbf{2 = ab^{-2}}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%20%3D%20ab%5E%7B-2%7D%7D)
![\mathbf{2 =a(2^{-2})}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%20%3Da%282%5E%7B-2%7D%29%7D)
This gives
![\mathbf{2 =a(\frac 14)}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%20%3Da%28%5Cfrac%2014%29%7D)
Multiply both sides by 4
![\mathbf{a = 8}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba%20%3D%208%7D)
Substitute 8 for (a) and 2 for (b) in ![\mathbf{y = ab^x}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20ab%5Ex%7D)
![\mathbf{y = 8(2)^x}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%208%282%29%5Ex%7D)
Express as a function
![\mathbf{g(x) = 8(2)^x}](https://tex.z-dn.net/?f=%5Cmathbf%7Bg%28x%29%20%3D%208%282%29%5Ex%7D)
Hence, the function g(x) is ![\mathbf{g(x) = 8(2)^x}](https://tex.z-dn.net/?f=%5Cmathbf%7Bg%28x%29%20%3D%208%282%29%5Ex%7D)
Read more about exponential functions at:
brainly.com/question/11487261
The answer would be 483,972 miles = 55