The article "Lead Dissolution from Lead Smelter Slags Using Magnesium Chloride Solutions" (A. Xenidis, T. Lillis, and I. Hallikia, The AusIMM Proceedings, 1999:37-44) discusses an investigation of leaching rates of lead in solutions of magnesium chloride. The data in the following table (read from a graph) present the percentage of lead that has been extracted at various times (in minutes).


a. The article suggests fitting a quadratic model y = β0 +β1t +β2t2 +ε to these data. Fit this model, and compute the standard deviations of the coefficients.
b. The reaction rate at time t is given by the derivative dy/dt = β1 +2β2t. Estimate the time at which the reaction rate will be equal to 0.05.
c. The reaction rate at t = 0 is equal to β1. Find a 95% confidence interval for the reaction rate at t = 0.
d. Can you conclude that the reaction rate is decreasing with time? Explain.