If the exponential function [tex]y=ab^x[/tex] passes through the points (3,25) and (8,10), the value of b is 0.833
The given exponential equation is:
[tex]y=ab^x[/tex]
The function passes through the points (3, 25) and (8, 10)
Substitute x = 3 and y = 25 into the function [tex]y=ab^x[/tex]
[tex]25=ab^3[/tex]............................(1)
Substitute x = 8 and y = 10 into the function [tex]y=ab^x[/tex]
[tex]10=ab^8[/tex].............................(2)
Divide equation (2) by equation (1)
[tex]\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[/tex]
Therefore, if the exponential function [tex]y=ab^x[/tex] passes through the points (3,25) and (8,10), the value of b is 0.833
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