Questions: How can the coffee's temperature after 19 minutes be found? Select the correct choice below and fill in the answer box to complete your choice. A. Evaluate T(). B. Solve =18+49 e^(-0.029 t) for t. The coffee's temperature after 19 minutes is °C. (Type an integer or decimal rounded to one decimal place as needed.)

How can the coffee's temperature after 19 minutes be found? Select the correct choice below and fill in the answer box to complete your choice.
A. Evaluate T().
B. Solve =18+49 e^(-0.029 t) for t.

The coffee's temperature after 19 minutes is °C.
(Type an integer or decimal rounded to one decimal place as needed.)

Transcript text: How can the coffee's temperature after 19 minutes be found? Select the correct choice below and fill in the answer box to complete your choice. A. Evaluate $T(\square)$. $\square$ B. Solve $\square=18+49 e^{-0.029 t}$ for t . The coffee's temperature after 19 minutes is $\square$ ${ }^{\circ} \mathrm{C}$. (Type an integer or decimal rounded to one decimal place as needed.)

Solution

Solution Steps

To find the coffee's temperature after 19 minutes, we need to evaluate the given temperature function at $ t = 19 $.

Solution Approach

Identify the temperature function $ T(t) = 18 + 49 e^{-0.029 t} $.
Substitute $ t = 19 $ into the function to find the temperature.

Step 1: Identify the Temperature Function

The temperature of the coffee as a function of time $ t $ is given by the equation: \[ T(t) = 18 + 49 e^{-0.029 t} \]

Step 2: Substitute $ t = 19 $

To find the temperature after 19 minutes, we substitute $ t = 19 $ into the temperature function: \[ T(19) = 18 + 49 e^{-0.029 \cdot 19} \]

Step 3: Calculate the Exponential Term

First, we calculate the exponent: \[ -0.029 \cdot 19 = -0.551 \] Then, we find $ e^{-0.551} $: \[ e^{-0.551} \approx 0.5769 \]

Step 4: Compute the Temperature

Now we can compute the temperature: \[ T(19) = 18 + 49 \cdot 0.5769 \approx 18 + 28.2851 \approx 46.2851 \] Rounding this to one decimal place gives: \[ T(19) \approx 46.3 \]