Answer:
Not sure
Step-by-step explanation:
Answer:
![f(x) = \frac{24}{25} * \frac{5}{6}^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B24%7D%7B25%7D%20%2A%20%5Cfrac%7B5%7D%7B6%7D%5Ex)
Step-by-step explanation:
Given
![(x_1,y_1) = (2,\frac{2}{3})](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%282%2C%5Cfrac%7B2%7D%7B3%7D%29)
![(x_2,y_2) = (3,\frac{5}{9})](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%283%2C%5Cfrac%7B5%7D%7B9%7D%29)
Required
Write the equation of the function ![f(x) = ab^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ab%5Ex)
Express the function as:
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
In: ![(x_1,y_1) = (2,\frac{2}{3})](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%282%2C%5Cfrac%7B2%7D%7B3%7D%29)
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
--- (1)
In ![(x_2,y_2) = (3,\frac{5}{9})](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%283%2C%5Cfrac%7B5%7D%7B9%7D%29)
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
--- (2)
Divide (2) by (1)
![\frac{5}{9}/\frac{2}{3} = \frac{a*b^3}{a*b^2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D%2F%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7Ba%2Ab%5E3%7D%7Ba%2Ab%5E2%7D)
![\frac{5}{9}/\frac{2}{3} = b](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D%2F%5Cfrac%7B2%7D%7B3%7D%20%3D%20b)
![\frac{5}{9}*\frac{3}{2} = b](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D%2A%5Cfrac%7B3%7D%7B2%7D%20%3D%20b)
![\frac{5}{3}*\frac{1}{2} = b](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7D%2A%5Cfrac%7B1%7D%7B2%7D%20%3D%20b)
![\frac{5}{6} = b](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7D%20%3D%20b)
![b = \frac{5}{6}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B5%7D%7B6%7D)
Substitute 5/6 for b in (1)
![\frac{2}{3} = a * b^2](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%3D%20a%20%2A%20b%5E2)
![\frac{2}{3} = a * \frac{5}{6}^2](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%3D%20a%20%2A%20%5Cfrac%7B5%7D%7B6%7D%5E2)
![\frac{2}{3} = a * \frac{25}{36}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%3D%20a%20%2A%20%5Cfrac%7B25%7D%7B36%7D)
![a = \frac{2}{3} * \frac{36}{25}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%2A%20%5Cfrac%7B36%7D%7B25%7D)
![a = \frac{2}{1} * \frac{12}{25}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B2%7D%7B1%7D%20%2A%20%5Cfrac%7B12%7D%7B25%7D)
![a = \frac{24}{25}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B24%7D%7B25%7D)
The function: ![f(x) = ab^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ab%5Ex)
![f(x) = \frac{24}{25} * \frac{5}{6}^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B24%7D%7B25%7D%20%2A%20%5Cfrac%7B5%7D%7B6%7D%5Ex)
Answer:
It's - 17x trust me it's right
Answer:
31/24
Step-by-step explanation:
multiple 2 by 24, then add 17, which you get 31, and put it over 24
31/24