From the options, the function has the next form
[tex]y=a\cdot b^x[/tex]
where a and b are two constants.
The function pass through the point (0, 2), then:
[tex]\begin{gathered} 2=a\cdot b^0 \\ 2=a\cdot1 \\ 2=a \end{gathered}[/tex]
The function pass through the point (1, 10), then:
[tex]\begin{gathered} 10=2\cdot b^1 \\ \frac{10}{2}=b \\ 5=b \end{gathered}[/tex]
Therefore, the function is:
[tex]y=2\cdot5^x^{}[/tex]
