Question

The speed of jogger varies as she runs with points (t, tracking her speed (miles per hours) after minutes of jogging: $(1,5.8),(6,6.3),(8,6.85)$

Find the first and second difference between the three points First differences: Second difference

Answer 1

Step-1: Finding first and second difference between these points:

The difference between the consecutive $y$ values is called the second difference.

For example, if we have $3$$y$ consecutive values as $5,10\&17$.

The difference between the consecutive pairs are $10-5=5\&17-10=7$

Therefore, the second difference is $7-5=2$

Step-2: Finding the differences:

Now we have three points given as $(1,5.8),(6,6.3),(8,6.85)$

The first difference is ,

$$\begin{gathered} 6.3-5.8=0.5\& \\ 6.85-6.3=0.55 \end{gathered}$$

The second difference will be equal to

$0.55-0.5=0.05$

Therefore, the first difference is equal to $0.5\&0.55$ and second difference is equal to $0.05$.