The rate of change of the temperature of a frozen brick is proportional to 70 Twhere T is temperature and m is measured in minutes. What is the differential equation to solve for T(m)? 0 =k(70+T) (in: :11" _ k 0 dm _ (70+T) o E =k(7UT) = k rim (7051") A loaf of bread is 200 degrees Fahrenheit when it is removed from the oven, and the rate of change of the temperature of the bread, B(t), as it cools is inversely proportional to B, where t is measured in minutes. What is the differential equation to solve for B? Donotsolve. O g=kt 0 gsz os=% 0 ea The speed S (t) of a front load plow clearing a road is inversely proportional to the height of the material being cleared, H. What is the differential equation to solve for number of feet plowed, D(t), where S(t)is measured in feet per second and H is the height of material in feet? Note, speed, S(t), is the rate of change of distance, D(t) 0 %=kH dD_k O E_ O gzk O zi The mess in a house can be measured by M(t). Assume that at Mm) = U, the house starts out clean. Over time the rate of change in the mess is proportional to 100 M. A completely messy house has a value of 100. What is the particular solution of M(t), if k is a constant? 0 M = 100 + 100g\" 0 M = 100 100a\" 0 M = 100 + 1009.4\" 0 M = 100 1005'\" A rate of change of H is given by % = k (25 + B). When f= 0, H= 50. When t= 2, H =100. Solve for kwhere H > 25. O 0.458 O 0.346 O 0.255 O 0.144 5 7 The rate of change of / is inversely proportional to csc(x) . N(x), where (I 0. If N(0) = 6, and N(2) = 9, find N(5). O 12.708 O 12.186 O 11.25 O 10.678A rate of change of Wis given by dw dt = k(100 - W). When t = 0, the population W = 50, and when t = 1, W = 25. Solve for k when W