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Sagot :
Given:
The exponential function is expressed as,
[tex]f(x)=ab^x[/tex]Put the point (4,3) in the above function,
[tex]\begin{gathered} \text{Let,y}=ab^x \\ 3=ab^4\ldots\ldots\ldots.\ldots..(1) \end{gathered}[/tex]Put the point (7,8),
[tex]8=ab^7\ldots.\ldots(2)[/tex]Solve equation (1) for a,
[tex]\begin{gathered} 3=ab^4 \\ a=3b^{-4} \\ \text{Put it in equation (2)} \\ 8=ab^7 \\ 3b^{-4}b^7=8 \\ b^3=\frac{8}{3} \\ b=\frac{2}{\sqrt[3]{3}} \end{gathered}[/tex]The equation (1) becomes,
[tex]\begin{gathered} 3=ab^4 \\ 3=a(\frac{2}{\sqrt[3]{3}})^4 \\ 3=a\times\frac{2^4}{3^{\frac{4}{3}}} \\ a=\frac{3\times3^{\frac{4}{3}}}{2^4} \\ a=0.8113 \end{gathered}[/tex]So, the exponential function is,
[tex]\begin{gathered} f(x)=ab^x \\ f(x)=0.8113(\frac{2}{\sqrt[3]{3}})^x \\ f(x)=0.8113(1.3867)^x \end{gathered}[/tex]Answer:
[tex]f(x)=0.8113(1.3867)^x[/tex]
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