Chapter 9.7, Problem 2STP

For Exercises 1-4, choose the correct letter.

Which kind of function best models the set of data points $(-3,18),(-2,6),(-1,2),(0,11),(1,27)?$

F. linear

G. quadratic

H. exponential

I. none of the above

To determine

To find : Which type of function best model the given data, use differences or ratio.

Answer to Problem 2STP

Option (I) is correct.

Explanation of Solution

Given information :

The given set of data point is $\left(-3,18\right),\left(-2,6\right),\left(-1,2\right),\left(0,11\right)\left(1,27\right)$

Calculation :

To find the type of model from the given set of data use the followings:

1. If the first difference of the y values is common, then linear model fits the data
2. If the second difference of the y values is common, then quadratic model fit the data.
3. If the y values have the common ratio, then an exponential model fits he data.

For the given set of data, find the find difference of the y values:

  $\begin{array}{l}6-18=-12\\ 2-6=-4\\ 11-2=9\\ 27-11=16\end{array}$

Since, the first differences is not common, so find the second differences

  $\begin{array}{l}-4-\left(-12\right)=8\\ 9-\left(-4\right)=13\\ 16-9=7\end{array}$

Since, the second differences are not common, so find the ratios of y values.

  $\begin{array}{l}\frac{18}{6}=3\\ \frac{6}{2}=3\\ \frac{2}{11}=0.18\\ \frac{11}{27}=0.41\end{array}$

Since, the y values do not have common ratio. Therefore, the given set of data point are not exponential.

Hence,

Option (I) is correct.