If the exponential function
passes through the points (3,25) and (8,10), the value of b is 0.833
The given exponential equation is:
![y=ab^x](https://tex.z-dn.net/?f=y%3Dab%5Ex)
The function passes through the points (3, 25) and (8, 10)
Substitute x = 3 and y = 25 into the function ![y=ab^x](https://tex.z-dn.net/?f=y%3Dab%5Ex)
............................(1)
Substitute x = 8 and y = 10 into the function ![y=ab^x](https://tex.z-dn.net/?f=y%3Dab%5Ex)
.............................(2)
Divide equation (2) by equation (1)
![\frac{10}{25}=\frac{ab^8}{ab^3} \\\\0.4=b^5\\\\b=0.4^\frac{1}{5} \\\\b=0.4^{0.2}\\\\b=0.833](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B25%7D%3D%5Cfrac%7Bab%5E8%7D%7Bab%5E3%7D%20%20%5C%5C%5C%5C0.4%3Db%5E5%5C%5C%5C%5Cb%3D0.4%5E%5Cfrac%7B1%7D%7B5%7D%20%5C%5C%5C%5Cb%3D0.4%5E%7B0.2%7D%5C%5C%5C%5Cb%3D0.833)
Therefore, if the exponential function
passes through the points (3,25) and (8,10), the value of b is 0.833
Learn more on exponential functions here: brainly.com/question/12940982