Question

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

Answer 1

Given:

An exponential function

`y=ab^x`

for a graph that passes through (2, 1) and (3, 8).

To know:

Find exponential function.

Step-by-step explanation:

`f(x)=a^x`

Solution:

We will use given values (2, 1) and (3, 8) in function

For point (2, 1)

`\begin{gathered} y=ab^x \\ 1=ab^2 \end{gathered}`

At (3, 8)

`8=ab^3`

So,

`\begin{gathered} 8=ab^2* b \\ 8=1* b \\ b=8 \end{gathered}`

Now, from value b ,we can find a,

`a=(1)/(64)`

So,

`\begin{gathered} y=8*((1)/(64))^x \\ y=8^(1-2x) \end{gathered}`

Hence, this is the function.