Exponential and Loguibuic Functions
Evaluating an exponential function with base e that models a reak-world.
A can of soda is placed inside a cooler. As the soda cools, its temperature $T(x)$ in degrees Celsius is given by the following function, where $x$ is the number of minutes since the can was placed in the cooler.
\[
T(x)=-7+23 e^{-0.034 x}
\]

Find the initial temperature of the soda and its temperature after 20 minutes.
Round your answers to the nearest degree as necessary.
Initial temperature:
\[
\square{ }^{\circ} \mathrm{C}
\]

Temperature after 20 minutes: $\square^{\circ} \mathrm{C}$

Step 1 ：Substitute \(x = 0\) into the function \(T(x) = -7 + 23e^{-0.034 * x}\) to find the initial temperature of the soda.

Step 2 ：Calculate \(T(0) = -7 + 23e^{-0.034 * 0} = -7 + 23e^0 = -7 + 23 * 1 = -7 + 23 = 16\).

Step 3 ：\(\boxed{16}\) degrees Celsius is the initial temperature of the soda.

Step 4 ：Substitute \(x = 20\) into the function \(T(x) = -7 + 23e^{-0.034 * x}\) to find the temperature of the soda after 20 minutes.

Step 5 ：Calculate \(T(20) = -7 + 23e^{-0.034 * 20} = -7 + 23e^{-0.68} = -7 + 23 * 0.506 = -7 + 11.638 = 4.638\).

Step 6 ：Rounding to the nearest degree, the temperature of the soda after 20 minutes is approximately 5 degrees Celsius.

Step 7 ：So, \(\boxed{5}\) degrees Celsius is the temperature of the soda after 20 minutes.