Question

The scatter plot shows the number of stamps Katie collected in different months: Plot ordered pairs 1, 30 and 2, 70 and 3, 110 and 4, 150 and 5, 190 What is the approximate predicted number of stamps she collected in the 25th month?

Answer 1

The approximate predicted number of stamps she collected in the 25th month is 990.

Explanation:

The ordered pairs as on the scatter plot is given as:

(1, 30) (2, 70) (3, 110) (4, 150) and (5 , 190 )

Where the ordered pair represent the number of stamps collected in different months.

Clearly from the set of values we could clearly observe that the value is increasing by 40 each month from the previous month.

i.e. we could have a recursion formula as:

`a_(n+1)=a_(n)+40` n=1,2,3,....

Which could also be written as:

`a_(n+1)=a_(1)+40* n`

(since,

`a_(2)=a_1+40\\ \\a_(3)=a_2+40=a_1+40+40=a_1+40*2\\\\a_4=a_3+40=a_1+40*2+40=a_1+40*3` and so on

Note that here
`a_1=30`)

Where
`a_(n)` denotes the number of stamps in the previous month.

and
`a_(n+1)` denotes the number of stamps in the (n+1)th month.

Hence, the number of stamps she collected in the 25th month= 30+40×24=30+960=990.

Answer 2

Find the pattern out of :

30, 70, 110, 150, 190

You will find that is counting by adding 40 every time.

Just find how far away 5 is from 25 :

25-5 = 20 so 20 more months.

The months times 40 = 800.

Add 800 to 190 :

800 + 190 = 990.

1, 30 and 2, 70 and 3, 110 and 4, 150 and 5, 190.........25, 990.

Hoped I helped!