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Write an exponential function y=ab^x for a graph that passes through (2,1) and (3,8)

Sagot :

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.

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