The differential equation below models the temperature of a 95°C cup of coffee in a 21°C room, where 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 cup of coffee in °C, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 95°C.)

A cup of coffee contains about 100 𝑚𝑔 of caffeine. Caffeine is metabolized and leaves the bodyat a continuous rate of about 17% every hour. Write a differential equation for the amount, 𝐴,of caffeine in the body as a function of the number of hours, 𝑡, since the coffee was consumed

Find an equation expressing the temperature (in ºC) of the water in the container as afunction of the volume (cups) of cold water added

(1 point) A very large tank initially contains 100L of pure water. Starting at time t=0 a solution with a salt concentration of 0.7kg/L is added at a rate of 6L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 4L/min. Answer the following questions.1. Let y(t) be the amount of salt (in kilograms) in the tank after t minutes. What differential equation does y satisfy? Use the variable y for y(t).Answer (in kilograms per minute): dydt =

is proportional to the amount present. In a certain reaction, the change of the substance satisfies the differential equation𝑑𝑦𝑑𝑡 = -0.64ywhere y is measured in grams and t is measured in hours. If there are 90 grams of the substance when t = 0, how many grams will be left after the first hour?

Differential Equations