A) A jar of juice came out of the refrigerator at 8 a.m. and placed on the kitchen counter. The temperature of the refrigerator is 4C and that of the kitchen is 22C. An hour later, the temperature of the juice jar is 9C. Let T(t) be the temperature of the pot t hours after 8 h.

1)Assuming that the temperature of the pot obeys Newton's cooling law, give the exact formula for T(t).

2)What is the temperature of the pot at 1 p.m.? Give the answer to the nearer 0.1.

B)Cesium-137 has a half-life of 30 years. The initial sample is 200 mg.

1)Determine the mass m(t) that persists after t years.

2)What is the mass of Cesium-137 after 100 years?Round the response to the nearest integer.

3)When will the mass be reduced to 10 mg?Round the response to the nearest integer.

C) We consider the problem at initial value y'=0.2x+0.1y and y(3)=0.4

1) Apply Euler's method to approach y(4) in steps of h=0.5 .

Give your approximation for y(4) with an accuracy of 0.01 .

2) Apply Euler's method to approach y(4) in steps of h=0.25 .

Give your approximation for y(4) with an accuracy of 0.01 .