Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0C for all t > 0. In each of 9 through 12, find an expression for the temperature u(x, t) if the initial temperature distribution in the rod is the given function. Suppose that 2 = 1.u(x, 0) = x, 0 < x < 40

.Let's begin with the first question. What was the prediction given in the article in 1990 The wording in the book is somewhat vague. Specifically, the question is asking what the quadratic model predicted for the year 2035. So, since t=0 represents 1960, and we want to represent 2035, we will take the difference. That gives us: .Now we will look at the second question. Does this prediction for the year 2035 seem accurate The question is asking how the prediction given by the quadratic model (which uses data from 1960‐1990) compares with the prediction given by the linear model (which uses data from 1980‐2010) .Therefore, the prediction given by quadratic model is too high (when compared to the linear model). These models were developed using a procedure cal