Question

During a tunnel construction project, engineers used explosives to excavate partway into a mountain. Because of time constraints and environmental concerns, they later used a tunnel boring machine (TBM) to excavate the rest of the tunnel. The table shows the length of the completed tunnel, y, after different numbers of days, x, since the TBM started working.
Number of Days Length of Tunnel (feet)
0 225
5 350
20 725
30 975
55 1,600

The length of the completed tunnel can be calculated using what equation .
If the project will be completed 86 days after the TBM was introduced, the length of the completed tunnel will be feet.

Answer 1

The given values lie on a line with slope

... m = (975 -725)/(30 -20) = 250/10 = 25

The initial value shown gives the y-intercept, so the length can be calculated using the equation

... y = 25x +225

_____

The length after 86 days will be

... y = 25·86 +225 = 2375 . . . feet