How to cook the perfect egg 5 points As an egg cooks, the proteins first denature and then coagulate. When the temperature exceeds a critical point, reactions begin and proceed faster as the temperature increases. In the egg white, the proteins start to coagulate for temperatures above 63 "C, while in the yolk the proteins start to coagulate for temperatures above 70 C. For a sott-boiled egg, the white needs to have been heated long enough to coagulate at a temperature above 63 C, but the yolk should not be heated above 70 C. For a hard-boiled egg, the center of the yolk should be allowed to reach 70 C. The follawing formula expresses the time t it takes (in secands) for the center of the yolk to reach the temperature Ty (in degrees centigradej: 1n 10.76 To T Here, M, p, c, and K are properties of the egg: M is the mass, p is the density, c is the specific heat capacity, and K is the thermal conductivity. Relevant values are M 17 g for a small egg and M-67 g for a large egg 1.038 g-cm a c = 3.7 J . g 1 . K l and K = 5.4-10-3 w cmK i Furthermore, T. is the temperature (in degrees centigrace) ot the bolling water, and To is the original temperature (in cegrees centirade) of the egg betore being put in the water We wish to implement this formula, but first, let's define some intermediate terms to make things easier to program Now the tormula can be expressed as Implement the formula in a program, set T,-100 C and T, = 70C. . Compute t for a large egg taken from the fridge (T, 4C) in variable t-large-fridge Compute 1 for a large egg starting at room temperature (T, = 20C) in variable l_arue_rum Your submission should include at least two parts 1. larue fridye 2. t large roon math. 1ng provides the natural logarithm furnction. You should use the library value of pi as well