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Given:
An exponential function
[tex]y=ab^x[/tex]for a graph that passes through (2, 1) and (3, 8).
To know:
Find exponential function.
Explanation:
[tex]f(x)=a^x[/tex]Solution:
We will use given values (2, 1) and (3, 8) in function
For point (2, 1)
[tex]\begin{gathered} y=ab^x \\ 1=ab^2 \end{gathered}[/tex]At (3, 8)
[tex]8=ab^3[/tex]So,
[tex]\begin{gathered} 8=ab^2\times b \\ 8=1\times b \\ b=8 \end{gathered}[/tex]Now, from value b ,we can find a,
[tex]a=\frac{1}{64}[/tex]So,
[tex]\begin{gathered} y=8\times(\frac{1}{64})^x \\ y=8^{1-2x} \end{gathered}[/tex]Hence, this is the function.