Answer:
[tex]y=2^x+5[/tex]
Explanation:
From the graph, the points are best modeled using an exponential function.
Among the given options, Options 3 and 4 are exponential functions.
The third and fourth functions are tested below:
Option 3
[tex]\begin{gathered} y=2^x+5 \\ x=11:y=2^{11}+5=2053 \\ x=13:y=2^{13}+5=8197 \\ x=15:y=2^{15}+5=32773 \end{gathered}[/tex]
Option 4
[tex]\begin{gathered} y=4^x+8 \\ x=11:y=4^{11}+8=4144312 \\ x=13:y=4^{13}+8=67108872 \\ x=15:y=4^{15}+8=1073741832 \end{gathered}[/tex]
From the above, we can see that the function that best fits the data shown in the scatterplot is:
[tex]y=2^x+5[/tex]
