Respuesta :
ANSWER
Yes, it does.
EXPLANATION
We want to check if the data set displays an exponential behavior.
An exponential function is one in which the values of the range (y values) increase by a certain factor.
The general form of an exponential function is:
[tex]y=a\cdot b^x[/tex]where a is the starting value
b = factor.
Now, we have to compare the data set with this kind of function.
To do that, we have to find a mock function of the data set using the first two data points to test each x value (domain) for each y value.
Basically, we will replace x in the function with a value and see if we get the correct y.
Therefore, when x = 0:
[tex]\begin{gathered} y=a\cdot b^0 \\ y=a\cdot1 \end{gathered}[/tex]From the data set, we see that, when x = 0, y = 1:
[tex]\begin{gathered} \Rightarrow1=a\cdot1 \\ a=1 \end{gathered}[/tex]That is the value of a.
Now, let us try when x = 1:
[tex]\begin{gathered} \Rightarrow y=1\cdot b^1 \\ y=b \end{gathered}[/tex]From the data set, we see that, when x = 1, y = 3:
[tex]\begin{gathered} \Rightarrow3=b \\ b=3 \end{gathered}[/tex]Now, we can say that we have an exponential function to test with:
[tex]y=3^x[/tex]So, let us test for the remaining values of x and y and see if they match the function.
[tex]\begin{gathered} \text{when x = 2:} \\ y=3^2 \\ y=9 \\ \text{when x = 3:} \\ y=3^3 \\ y=27 \end{gathered}[/tex]As we can see, each x value that goes into the function yields the exact y value as the data set. This means that the exponential function works for it.
Hence, the data set displays an exponential behavior.
