# Calculus with Diffrential Equations: Pleease help?

posted by Bridget

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes.
A physical principle known as Newton’s Law of Cooling tells us that
dT/dt = -1/15T+5
15T + 5.
a) Supposes that T(0) = 105. What does the differential equation give us for the
value of dT
dt |T=0? Explain in a complete sentence the meaning of these two
facts.
(b) Is T increasing or decreasing at t = 0?
(c) What is the approximate temperature at t = 1?
(d) On a graph, make a plot of dT/dt as a function of T.
(e)For which values of T does T increase?
(f) What do you think is the temperature of the room? Explain your thinking.
(g) Verify that T(t) = 75 + 30e^(-t/15) is the solution to the differential equation with initial value T(0) = 105. What happens to this solution after a long time?

## Similar Questions

1. ### Calculus

The temperature of a cup of Starbucks coffee at time t (in minutes) is T(t)= 70 + c e^(-kt) . Initially, the temperature of the coffee was 200 degrees F. Three minutes later, it was 180 degrees. When will the temperature of the coffee …
2. ### Calculus

Suppose you have a hot cup of coffee in a room where the temp is 45 Celcius. Let y(t) represent the temp. of coffee as a function of the number of minutes t that have passed since the coffee was poured a) write a differential equation …
3. ### Calc

A cup of coffee at 90 degrees celsius is put into a 30 degree celsius room when t =0 . The coffee's temperature, f (t ) , is changing at a rate given by f '(t )=-8(0 .8) t degrees celsius per minute, where t is in minutes. Estimate …
4. ### Calculus

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + …
5. ### Differential equations in Calculus...plsssss help?

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + …
6. ### Pre-Calc/Trigonometry

You place a cup of 205oF coffee on a table in a room that is 72oF, and 10 minutes later, it is 195oF. Approximately how long will it be before the coffee is 180oF?
7. ### calculus

The temperature of a hard boiled egg varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus A, where T is the temperature of the egg, A is the room temperature, and k is a positive constant. …
8. ### math

A cup of coffee at 173 degrees is poured into a mug and left in a room at 72 degrees. After 6 minutes, the coffee is 137 degrees. Assuming that Newton's Law of Cooling applies: After how many minutes will the coffee be 100 degrees?
9. ### calculus

The differential equation below models the temperature of a 87°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 67°C. Solve the differential equation to …
10. ### Differential equations

Suppose a cup of coffee is at 100 degrees Celsius at time t = 0, it is at 70 degrees at t = 10 minutes, and it is at 50 degrees at t = 20 minutes. Compute the ambient temperature. So in the book I was given Newton's Heat equation. …

More Similar Questions