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# Easy rate question

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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.

Oct 31, 2020

#1
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(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

Oct 31, 2020
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Thanks a ton!

P.s. it's meters not feet

Mathulator  Oct 31, 2020
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Yah...meters, not feet... the equation does not change....

ElectricPavlov  Oct 31, 2020