Question

Write an exponential function whose graph passes through the given points.(0, 3) and (3, 375)

Answer 1

We need to write an exponential function with points (0,3) and (3,375).

So we can write:

`\begin{gathered} y=Ax^B \\ w\text{here A and B are constants} \end{gathered}`

For the points we have:

`\begin{gathered} y=3=A\cdot0^B\Rightarrow A=3 \\ y=375=A\cdot3^B=3\cdot3^B=3^(B+1) \\ \text{Taking log3:} \\ \log _3(375)=\log _3(3^(B+1))=(B+1)\cdot\log _33=B+1 \\ B=\log _3(375)-1 \end{gathered}`

We can find the log3(375) as:

`\begin{gathered} \log _3(375)=(\log _(10)(375))/(\log _(10)(3))=5.39 \\ B=\log _3(375)-1=4.39 \end{gathered}`

So, the equation is:

`y=3x^(4.39)`