Question

Graph the data set.

{(-1, 0.5), (0, 1), (1, 2), (3, 8), 5, 32)}
Which kind of model best describes the data?

a. quadratic
b. exponential
c. linear
d. cubic

Answer 1

b. Exponential

Explanation:

We are given the coordinates as the data set:

`\bold{\{(-1, 0.5), (0, 1), (1, 2), (3, 8), (5, 32)\}}`

First of all, let us plot the given coordinates on the xy coordinate axis.

Let us have a look at the values of x and y first.

A pair is represented as (x, y) i.e. first value is of 'x' and the second value is of 'y'.

`\begin{center}\begin{tabular}{ c c } x & y\\ -1 & 0.5 \\ 1 & 2 \\ 2 & 4 \\ 3 & 8 \\ 5 & 32\end{tabular}\end{center}`

If we plot them on the graph, we get the graph as the image attached in the answer area.

Let us join the coordinates using a curve.

If we closely look at the graph, there is a sudden increase with increasing value of 'x'.

Actually the increase is exponential.

Observing the given coordinates, we can see that they are in the form:

`(x, 2^x)`

i.e.
`y =2^x`

So, the exponential model best describes the data.

Correct answer is:

b. exponential