Question

Consider the following data set which relates the hemoglobin levels h (kg/dL) of workers and the altitude a (km) above the sea level that the workers exposed over years:
a 0.32 0.64 1.28 1.60
h 1.15 1.10 1.05 0.95

In the regression model h = c1e^-c2a, the constant c2 is found as c2 = 0.1315. Assuming the hemoglobin concentration for the residents at the highest permanently tolerable altitude of the atmosphere is the 1/1000th of the hemoglobin concentration for the residents at sea level, compute the highest permanently tolerable altitude in kilometers.

Answer 1

Answer:

The highest permanently tolerable altitude is 52.53 km.

Step-by-step explanation:

We have to calculate the maximum altitude that the residents/workers can tolerate.

This altitude is at which the hemoglobin conventration is 0.001 of the concentration at sea level.

We can express that as:

$\frac{h_{max}}{h_0}=\frac{c_1e^{-c_2a_{max}}}{c_1e^0} =e^{-c_2a_{max}}=0.001\\\\-c_2*a_{max}=ln(0.001)\\\\a_{max}=-ln(0.001)/c_2=6.9078/0.1315\\\\a_{max}=52.5308$

The highest permanently tolerable altitude is 52.53 km.