Hi Guys, I need to know how to create a function and graph using the data below. It shows the costs for a school trip to a school.
20 children = £100
21 = 95
22 = 90
23 = 85
24 = 80
25 = 75
26 = 70
27 = 65
28 = 60
29 = 55
30 = 150
31 = 176
32 = 172
33 = 168
34 = 164
35 = 160
36 = 156
37 = 152
38 = 148
39 = 144
40 = 240
41 = 277
42 = 274
43 = 271
44 = 268
45 = 265
46 = 262
47 = 259
48 = 256
49 = 253
50 = 250

As you can see the data is quite random. How can I tlk about this data in regards to functions and graphs?

31 = 145

2. Originally Posted by Berwick
Hi Guys, I need to know how to create a function and graph using the data below. It shows the costs for a school trip to a school.
20 children = £100
21 = 95
22 = 90
23 = 85
24 = 80
25 = 75
26 = 70
27 = 65
28 = 60
29 = 55
30 = 150
31 = 176
32 = 172
33 = 168
34 = 164
35 = 160
36 = 156
37 = 152
38 = 148
39 = 144
40 = 240
41 = 277
42 = 274
43 = 271
44 = 268
45 = 265
46 = 262
47 = 259
48 = 256
49 = 253
50 = 250

As you can see the data is quite random. How can I tlk about this data in regards to functions and graphs?

31 = 145
Plot the data as a scatter plot. Then decide on a model to use to fit the data. Then use technology to fit that model to the scatterplot. You might need to investigate several models - use the one that gives the largest value of r (the correlation coefficient). The value of r will be given to you by the technology you use.

3. ## Data and functions

Hello Berwick

If, as you say, the data is as random as that - and it seems nonsense that this should be the pattern of costs for a school trip - then you won't find a simple algebraic function to represent all the data.

But if you break it down into several ranges of values, you can find functions for each range.

So, suppose $\displaystyle n$ is the number of children going on the trip, and the cost is £$\displaystyle C$. Then in the range $\displaystyle 20\le n \ 29$, for each $\displaystyle 1$ that $\displaystyle n$ increases, $\displaystyle C$ decreases by $\displaystyle 5$. So $\displaystyle C$ will be in the form $\displaystyle A - 5n$. And when $\displaystyle n = 20, C = 100$. So $\displaystyle A = 200$.

So for $\displaystyle 20\le n \le 29, C = 200 - 5n$.

(Note that if there's a typo at $\displaystyle n = 30$, and it should read $\displaystyle C = 50$, then you can include $\displaystyle n = 30$ in this formula as well.)

In a similar way, if $\displaystyle 31 \le n \le 39$ (or $\displaystyle 40$ if there's a similar typo at $\displaystyle n = 40$), the formula you want is $\displaystyle C = 300 - 4n$.

And if $\displaystyle 41 \le n \le 50, C = 400 - 3n$.

As far as plotting a graph is concerned, what about using Excel?