Answer:
The predicted number of visitors in 2015 is 605.
Step-by-step explanation:
Since, the difference in number of visitors in consecutive year is approximately constant.
Thus, the function that shows the given situation can be linear.
Let x represents the number of years and y represents the visitors.
Now, suppose the estimation is started from 2003,
Hence, the table will be,
Year (x) 0 1 2 3 4 5
Visitors (y) 310 332 355 380 406 434
By the above table,
[tex]\sum x = 15[/tex]
[tex]\sum y = 2217[/tex]
[tex]\sum x^2 = 55[/tex]
[tex]\sum xy = 5976[/tex]
Since, the equation of a linear function is,
y = b + ax
Where,
[tex]a=\frac{\sum y \sum x^2 - \sum x \sum xy}{n(\sum x^2)-(\sum x)^2}[/tex]
And,
[tex]b=\frac{n(\sum xy) - \sum x \sumy}{n(\sum x^2)-(\sum x)^2}[/tex]
Where, n is the number of observation,
Here, n = 6,
By putting the values,
We get, a = 24.77142857 ≈ 24.77 and b = 307.5714286≈ 307.57
Thus, the equation that shows the given table is,
y = 24.77 x + 307.57
For 2015, x = 12,
⇒ y = 24.77 × 12 + 307.57 = 604.81 ≈ 605.
Hence, the predicted number of visitors = 605.
