A weather balloon's altitude in meters after t minutes is given by the function A(t) = 100… — ACT

A weather balloon's altitude in meters after $t$ minutes is given by the function $A(t) = 100 + 50t$ . The air temperature in degrees Celsius at an altitude of $a$ meters is modeled by the function $T(a) = 25 - 0.02a$ . What is the temperature of the air surrounding the balloon, in degrees Celsius, after $2$ minutes?

Answer: 21 degrees Celsius

Answer

The temperature of the air surrounding the balloon after 2 minutes is 21 degrees Celsius.

The temperature of the air surrounding the balloon after 2 minutes is found by first calculating the balloon's altitude,

A(2) = 100 + 50(2) = 200

meters, and then using this altitude to evaluate the temperature function,

T(200) = 25 - 0.02(200) = 21

Step-by-Step Solution

Calculate the altitude of the weather balloon at

t = 2

minutes using the function

A(t)

A(2) = 200

meters

To find the temperature surrounding the balloon, we must first determine its altitude at the given time of 2 minutes.

Substitute the altitude of 200 meters into the temperature function

T(a)

T(200) = 21

degrees Celsius

The temperature function depends on the altitude, so evaluating

T(200)

yields the temperature at that height.

Key Concept

Evaluating composite functions in a real-world context.

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