A container of hot liquid is placed in a freezer that is kept at a constant temperature of 20°F. The initial temperature of the liquid is 160°F. After 5 minutes, the liquid's temperature is 60°F. dy dt (a) Let y represent the temperature of the liquid in degrees Fahrenheit and let t represent the time in minutes after it is placed in the freezer. Write a differential equation (Use k for the constant of proportionality.) k(y-20) dy dt Find the general solution of the differential equation. (Use k for the constant of proportionality. Use C for any needed constant.) y = 20+ Cekt Use the given initial temperature to find the particular solution of the differential equation. 20+140 (3m (3)) y = X (b) How much longer will it take for its temperature to decrease to 27°F? (Round your answer to two decimal places.) 9.07 X min
A container of hot liquid is placed in a freezer that is kept at a constant temperature of 20°F. The initial temperature of the liquid is 160°F. After 5 minutes, the liquid's temperature is 60°F. dy dt (a) Let y represent the temperature of the liquid in degrees Fahrenheit and let t represent the time in minutes after it is placed in the freezer. Write a differential equation (Use k for the constant of proportionality.) k(y-20) dy dt Find the general solution of the differential equation. (Use k for the constant of proportionality. Use C for any needed constant.) y = 20+ Cekt Use the given initial temperature to find the particular solution of the differential equation. 20+140 (3m (3)) y = X (b) How much longer will it take for its temperature to decrease to 27°F? (Round your answer to two decimal places.) 9.07 X min
A container of hot liquid is placed in a freezer that is kept at a constant temperature of 20°F. The initial temperature of the liquid is 160°F. After 5 minutes, the liquid's temperature is 60°F. dy dt (a) Let y represent the temperature of the liquid in degrees Fahrenheit and let t represent the time in minutes after it is placed in the freezer. Write a differential equation (Use k for the constant of proportionality.) k(y-20) dy dt Find the general solution of the differential equation. (Use k for the constant of proportionality. Use C for any needed constant.) y = 20+ Cekt Use the given initial temperature to find the particular solution of the differential equation. 20+140 (3m (3)) y = X (b) How much longer will it take for its temperature to decrease to 27°F? (Round your answer to two decimal places.) 9.07 X min
Use the given initial temperature to find the particular solution of the differential equation. And solve for (b)
Transcribed Image Text:dy
dt
A container of hot liquid is placed in a freezer that is kept at a constant temperature of 20°F. The initial temperature of the liquid is 160°F. After 5 minutes, the liquid's temperature is 60°F.
(a) Let y represent the temperature of the liquid in degrees Fahrenheit and let t represent the time in minutes after it is placed in the freezer. Write a differential equation
the constant of proportionality.)
k(y – 20)
dy
dt
Find the general solution of the differential equation. (Use k for the constant of proportionality. Use C for any needed constant.)
20+ Cekt
y =
=
Use the given initial temperature to find the particular solution of the differential equation.
( ½-¹m ( ²/7 ) )
y =
20+ 140e
(b) How much longer will it take for its temperature to decrease to 27°F? (Round your answer to two decimal places.)
9.07
X min
(Use k for
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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