The formula for the temperature at height h with ground temperature of .
The formula for temperature at height h is .
The air cools at the rate of for each at height and rise up to a distance of the ground temperature is .
Since the air cools at the rate of for each height, at height the temperature is which is .
At height , the temperature will be which is .
Let the height be h.
At height h, then the value for temperature will be as follows:
Therefore, the formula for temperature at height h is .
The range of temperature if the plane takes off and reaches a maximum height of .
The range for the temperature is .
From part (a), the formula for temperature at height h is .
It is given that it reaches a maximum height of 5 km. That is, .
Convert 5 km to meters as follows:
Also, let the minimum height be 0 m. That is, .
Simplify as follows:
Substitute in and obtain the range of temperature as follows:
Reverse the inequality by diving by –1 as follows:
Therefore, the range for the temperature is .
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