Solve using table of values
The Winter Sports Shoppe has seen a steady increase in the sales of snowboards over the last three years . They sold 120 snowboards the first year, 280 the second year, and 440 this year. If the pattern continues, how many snowboards might they sell in the sixth year ?
* I know the answer just not sure how to set up the table*
just make a table with two columns
Each column will have a row for the year # and its associated sales
Mark years with x and sold snowboards with y.
x1 = 1 , y1 = 120
x2 = 2 , y2 = 280
x3 = 3 , y = 440
y2 - y1 = 280 - 120 = 160
y3 - y2 = 440 - 280 = 160
Difference is constant.
This mean, equation is linear , y = m x + c
m is the slope of the line.
m = ( y2 - y1 ) / ( x2 -x1 )
In this case:
m = ( 280 - 120 ) / ( 2 -1 )
m = 160 / 1 = 160
Replace this value in equation:
y = m x + c
y = 160 x + c
Put x = 1 , y = 120 in equation y = 160 x + c
120 = 160 ∙ 1 + c
120 = 160 + c
120 - 160 = c
c = - 40
Your function is:
y = 160 x - 40
In the sixth year x = 6
y = 160 x - 40
y = 160 ∙ 6 - 40
y = 960 - 40 = 920
Of course, you can also create a table.
The difference is a constant = 160 and you just put in the table:
year is the previous year + 1
sales = sales of in previes year + 160
The table looks like this.
1 | 120
2 | 280
3 | 440
4 | 600
5 | 760
6 | 920
To set up the table of values, let's start by listing the years and the corresponding number of snowboards sold:
| Year | Number of Snowboards Sold |
|------|---------------------------|
| 1 | 120 |
| 2 | 280 |
| 3 | 440 |
Now, let's observe the pattern. We can see that the number of snowboards sold is increasing by the same difference each year.
To find this difference, we subtract the number of snowboards sold in the first year from the number sold in the second year:
280 - 120 = 160
And to find the difference between the second and third year, we subtract the number of snowboards sold in the second year from the number sold in the third year:
440 - 280 = 160
Since the difference is the same, we can assume that the pattern will continue, and the difference will remain constant in the upcoming years.
Now, let's use this difference to predict the number of snowboards that might be sold in the sixth year.
To find the difference between the third and fourth year, we subtract the number of snowboards sold in the third year from the number sold in the fourth year:
440 + 160 = 600
And to find the difference between the fourth and fifth year:
600 + 160 = 760
Finally, to find the difference between the fifth and sixth year, we add the difference to the number of snowboards sold in the fifth year:
760 + 160 = 920
Therefore, it is predicted that the Winter Sports Shoppe might sell 920 snowboards in the sixth year, assuming the pattern continues.