When digging into the earth, the temperature 100 m deep is 16 degrees celsius, and at 850 m deep the temperature is 23.5 degrees celsius.
Assuming that the temperature can be approximated by a linear equation, write an equation for the Temperature (T) at depth (D).
In this equation, what is the meaning of the value of the slope?
Assuming a constant rate of change, estimate the depth at which we would find the temperature of 100 degrees celsius.
(x,y) = 100,16 and 850 , 23.5
slope = (16-23.5)/(100-850) = .01
y = .01 x + b Plug in a point ot calculate b
16 = .01 (100) + b b = 15
to = .01 d + 15 t = temp d = depth
Slope tells you the temperature gradient .... each additional 100 ft of depth = 1 degree warmer
Last part: 100 = .01(d) + 15 solve for d at which t = 100o C