a freezer has a temperature of 14 degrees fahrenheit. an ice - cube tray full of water is placed in the…

a freezer has a temperature of 14 degrees fahrenheit. an ice - cube tray full of water is placed in the freezer. the function f(t)=ce^(-kt)+14 represents the temperature of the water after t minutes, where k = 0.045 and c is a constant. if a tray of water was placed in the freezer, after 15 minutes the water has a temperature of 40 degrees. what was the initial temperature of the water. round your answer to the nearest degree. enter the solution as a decimal number round to the nearest tenth digit.

a freezer has a temperature of 14 degrees fahrenheit. an ice - cube tray full of water is placed in the freezer. the function f(t)=ce^(-kt)+14 represents the temperature of the water after t minutes, where k = 0.045 and c is a constant. if a tray of water was placed in the freezer, after 15 minutes the water has a temperature of 40 degrees. what was the initial temperature of the water. round your answer to the nearest degree. enter the solution as a decimal number round to the nearest tenth digit.

Answer

Explanation:

Step1: Sustituir valores en la función

Dado que $f(t)=Ce^{-kt}+14$, $k = 0.045$, $t = 15$ y $f(15)=40$. Sustituimos en la ecuación: $40=Ce^{-0.045\times15}+14$

Step2: Simplificar la ecuación

Primero, calculamos $-0.045\times15=-0.675$. Entonces la ecuación es $40=Ce^{- 0.675}+14$. Restamos 14 de ambos lados: $40 - 14=Ce^{-0.675}$ $26=Ce^{-0.675}$

Step3: Despejar la constante C

Sabemos que $e^{-0.675}\approx0.5091$. Entonces $C=\frac{26}{e^{-0.675}}=\frac{26}{0.5091}\approx51.07$.

Step4: Encontrar la temperatura inicial

La temperatura inicial es cuando $t = 0$. Sustituimos $t = 0$ en $f(t)=Ce^{-kt}+14$. Como $e^{-k\times0}=e^{0}=1$, entonces $f(0)=C + 14$. Sustituyendo $C\approx51.07$, tenemos $f(0)=51.07+14=65.07\approx65.1$

Answer:

$65.1$