Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. Let k>0 be the constant of proportionality. Assume the coffee has a temperature of 200 degrees Fahrenheit when freshly poured, and 11 minutes later has cooled to 190 degrees in a room at 62 degrees. Required:
a. Write an initial value problem for the temperature T of the coffee, in Fahrenheit, at time t in minutes.
b. Solve the initial value problem in part (a).

Tt = Ts + Ce^-kt

Tt = 62 + 138e^-0.0068t

Step-by-step explanation:

The initial value problem for the Newton cooling rate is :

Tt = Ts + Ce^-kt

Initial temperature,when freshly poured Ti = 200°F

Temperature after 11 minutes = 190°F

Temperature of room, Ts= 62°F

Using the relation :

Tt = Ts + Ce^-kt

Temperature after time, t

When freshly poured, t = 0

k = constant of proportionality

We can then solve for C and k as follows :

200 = 62 + Ce^-0k

200 = 62 + C

C = 200 - 62 = 138°F

Using the Temperature after 11 minutes ; we can find, k, proportionality constant:

Temperature, Tt after, t = 11 minutes = 190

Tt = Ts + Ce^-kt

190 = 62 + 138e^-11k

128 = 138e^-11k

128 / 138 = e^-11k

0.9275 = e^-11k

Take In of both sides :

−0.075223 = - 11k

k = −0.075223 / - 11

k = 0.0068

The model function becomes :

Ts = 62 ; C = 138

Tt = 62 + 138e^-0.0068t

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

sorry i need the points

step-by-step explanation:

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