contestada

14.
A
B
C
The Fahrenheit temperature, F(t), of a heated object at time t,
in minutes, can be modeled by the function below. F, is the
surrounding temperature, Fo is the initial temperature of the object.
and k is a constant.
F(t) = F₂ + (F₁-F₂)e¯kt
Coffee at a temperature of 195°F is poured into a container. The
room temperature is kept at a constant 68°F and k = 0.05. Coffee
is safe to drink when its temperature is, at most, 120°F. To the
nearest minute, how long will it take until the coffee is safe to drink?
10
E
18

Respuesta :

ashishdwivedilVT

It will take 18 minutes until the coffee is safe to drink.

What is Exponential Function?

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round.

Here, given equation

      F(t) = F₂ + (F₁-F₂)[tex]e^{-kt}[/tex]

F₂ = 68⁰F      F₁ = 195°F       F(t) = 120⁰F,       k = 0.05

     120 = 68 + (195 - 68) [tex]e^{-0.05t}[/tex]

      [tex]e^{-0.05t}[/tex] = 52/127

     [tex]e^{-0.05t}[/tex] = 0.4094

     -0.05t = ln (0.4094)

       -0.05 t = -0.839

           t ≈ 18

Thus, It will take 18 minutes until the coffee is safe to drink.

Learn more about Exponential function from:

https://brainly.com/question/11487261

#SPJ1

Otras preguntas