Questions: A 12-oz can of soda is put into a refrigerator to cool. Its temperature in Fahrenheit after (t) minutes is given by the following formula: [ T=38+36 e^-.02 t ] What is the eventual temperature of the soda?

Solution Steps

To find the eventual temperature of the soda, we need to determine the limit of the temperature function \( T \) as \( t \) approaches infinity. As \( t \) increases, the exponential term \( e^{-.02 t} \) will approach zero. Therefore, the eventual temperature will be the constant term in the equation.

The temperature \( T \) of the soda after \( t \) minutes is given by the formula: \[ T = 38 + 36 e^{-0.02 t} \]

To find the eventual temperature, we need to evaluate the limit of \( T \) as \( t \) approaches infinity: \[ \lim_{t \to \infty} T = \lim_{t \to \infty} \left( 38 + 36 e^{-0.02 t} \right) \] As \( t \) increases, the term \( e^{-0.02 t} \) approaches \( 0 \). Therefore, we have: \[ \lim_{t \to \infty} T = 38 + 36 \cdot 0 = 38 \]

The eventual temperature of the soda is \( 38 \) degrees Fahrenheit.

Final Answer