The given data can be tabulated as:
number of days,x length
of tunnel (ft), y
0 225
5 350
20 725
30 975
55 1,600
To check if the growth is linear, the slope at points (0,
225) and (5, 350), and (0, 225) and (20, 725) should be equal. The formula for
slope is:
m = (y2 – y1) / (x2 – x1)
Finding for slope (0, 225) and (5, 350):
m = (350 – 225) / (5 – 0) = 25
Finding for slope (0, 225) and (20, 725):
m = (725 – 225) / (20 – 0) = 25
Therefore the equation is linear in the form of:
y = mx + b
where b is the value of y at x = 0, so b = 225
The complete equation is:
y = 25x + 225
At x = 86 days
y = 25(86) + 225
y = 2,375 ft
Therefore the length of the completed tunnel is 2,375
feet.
