# math

Newton’s law of cooling states that for a cooling substance with initial temperature T0, the temperature T(t) after t minutes can be modeled by the equation T(t)=Ts+(T0−Ts)e−kt, where Ts is the surrounding temperature and k is the substance’s cooling rate.

A liquid substance is heated to 80°C. Upon being removed from the heat, it cools to 60°C in 15 min.

What is the substance’s cooling rate when the surrounding air temperature is 50°C?

Round the answer to four decimal places.

0.0687
0.0732
0.0813
0.0872

1. 👍
2. 👎
3. 👁
1. I guessed 0.0813 which was wrong. The answer is 0.0732

1. 👍
2. 👎
2. so why did you guess? They gave you the formula and the data point.
T(15) = 60, so
50 + 30e^(-15k) = 60
k = ln3/15 = 0.0732

1. 👍
2. 👎
👤
oobleck

## Similar Questions

1. ### Calculus

The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT/dt = -k(T - A), where T is the temperature of the tea, A is the room temperature, and k is a positive constant. If the water cools from 100°C to

2. ### Math

Using Netwon Law of Cool, the graph of T(t)=S+(T subscript --S)e^kt approaches a horizontal asymptote.What does the asymtote describe? a) intial temperature of the heated object b) temperature of the surrounding environment c) the

3. ### Chemistry

4. A typical car engine produces 44,000 kJ of heat in an hour. The cooling system has a capacity of 8.40 L and is filled with a 50:50 mixture of anti-freeze (specific heat capacity of 8.37 J/g-oC, density of 1.038 g/mL). In

4. ### College Algebra Application

Newton's Law of Cooling T(t)=T0+(T1-T0)e^-kt The police discover the body of a murder victim. Critical to solving the crime is determining when the murder was committed. The coroner arrives at the murder scene at 12:00pm. She

1. ### Physics

A 5000 kg African elephant has a resting metabolic rate of 2500 W. On a hot day, the elephant's environment is likely to be nearly the same temperature as the animal itself, so cooling by radiation is not effective. The only

2. ### algebra

According to Newton's law of cooling, the rate at which an object cools is directly proportional to the difference in temperature between the object and the surrounding medium. The face of a household iron cools from 135° to

Newton’s law of cooling states that for a cooling substance with initial temperature T0 T 0 , the temperature T(t) T ( t ) after t minutes can be modeled by the equation T(t)=Ts+(T0−Ts)e−kt T ( t ) = T s + ( T 0 − T s ) e

4. ### Chemistry

Check my work & answer please. I need to make sure I am able to do this type of problem correctly. A typical car engine produces 44,000 kJ of heat in an hour. The cooling system has a capacity of 8.40 L and is filled with a 50:50

1. ### ALGEBRA

A transformer has cooling fans that are set to come on when the temperature reaches 32° Celsius. The temperature is 90° Fahrenheit. Are the fans running?

2. ### calculus

A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 71°C, it is cooling at a rate of 1°C per minute. When does this occur?

3. ### algebra

A body was found at 10 a.m in a warehouse where the temperature was 40 degrees Fahrenheit. The medical examiner found the temperature of the body to be 80 degrees Fahrenheit. What is the approximate time of death? Use Newtons law

4. ### Math

Consider a 92∘C cup of coffee placed in a 24∘C room. Suppose it is known that the coffee cools at a rate of 2∘C/min when it is 70∘C. Then according to Newton's law of cooling, the temperature T(t) of the coffee t minutes