Question

Which of the following functions best fits the data shown in the scatterplot below?

Answer 1

`y=2^x+5`

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

`\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}`

Option 4

`\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}`

From the above, we can see that the function that best fits the data shown in the scatterplot is:

`y=2^x+5`