Maths(exp function)

2008-09-01 11:25 pm

Aircrafts require longer takeoff distances, called takeoff rolls, at high altitude airports because of diminished air density. The table shows how the takeoff roll for a certain light airplane depends on the airport elevation. (Takeoff rolls are also strongly influenced by air temperature; the data shown assume a temperature of 0 ºC.) Determine a formula for this particular aircraft that gives the takeoff roll as an exponential function of airport elevation. (Note: Use the general exponential function.)

更新1:

Elevation (ft)~~~Sea level~1000~~2000~~3000~~4000 Take off roll (ft)~~665~~~~729~~799~~~875~~~960 find d(h) = ?

回答 (1)

用戶10012

2008-09-02 8:04 pm

✔ 最佳答案

Let takeoff roll = T and Elevation = E. Therefore,
T = A10^(kE), where A and k are constants.
log T = log [A10^(kE)]= log A + log 10^(kE) = log A + kE.............(1)
When E = 0, T = 665, so log T = 2.8228. From (1), we get
2.8228 = log A + k(0), therefore, log A = 2.8228, so A = 665.
When E = 1000, T = 729, therefore from (1),
log 729 = 2.8228 + k(1000)
2.8627 = 2.8228 + 1000K
k = 0.0399/1000. Therefore,
T = 665x 10^(0.00004E).

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