We need to write an exponential function with points (0,3) and (3,375).
So we can write:
[tex]\begin{gathered} y=Ax^B \\ w\text{here A and B are constants} \end{gathered}[/tex]For the points we have:
[tex]\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}[/tex]We can find the log3(375) as:
[tex]\begin{gathered} \log _3(375)=\frac{\log _{10}(375)}{\log _{10}(3)}=5.39 \\ B=\log _3(375)-1=4.39 \end{gathered}[/tex]So, the equation is:
[tex]y=3x^{4.39}[/tex]