The differential equation below models the temperature of an 89°C cup of coffee in a 21°C room, where t is the time in minutes. It is known that the coffee cools at a rate of 1°C per minute when its temperature is 71°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let Y be the temperature of the coffee when the temperature was 89°C.) $$ \frac{dy}{dt} = -\frac{1}{50}(y - 21) $$

Name: the differential equation below models the temperature of an 89c cup of coffee in a 21c room where t is the time in minutes it is known that the coffee cools at a rate of 1c per minute when 38798
Uploaded: 2023-03-30T14:45:29-08:00
Duration: 1 min 17 s
Channel: Madhur L
Description: the differential equation below models the temperature of an 89c cup of coffee in a 21c room where t is the time in minutes it is known that the coffee cools at a rate of 1c per minute when 38798

          The differential equation below models the temperature of an 89°C cup of coffee in a 21°C room, where t is the time in minutes. It is known that the coffee cools at a rate of 1°C per minute when its temperature is 71°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let Y be the temperature of the coffee when the temperature was 89°C.)

$$ \frac{dy}{dt} = -\frac{1}{50}(y - 21) $$

the differential equation below models the temperature of an 89c cup of coffee in a 21c room where t is the time in minutes it is known that the coffee cools at a rate of 1c per minute when 38798

Added by Jose Miguel K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

03/30/2023

Step 1

We can separate the variables y and t: $$ \frac{dy}{y - 21} = -\frac{1}{50} dt $$ Show more…

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The differential equation below models the temperature of an 89°C cup of coffee in a 21°C room, where t is the time in minutes. It is known that the coffee cools at a rate of 1°C per minute when its temperature is 71°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let Y be the temperature of the coffee when the temperature was 89°C.) $$ \frac{dy}{dt} = -\frac{1}{50}(y - 21) $$