The article “Lead Dissolution from Lead Smelter Slags Using Magnesium Chloride Solutions” (A. Xenidis, T. Lillis, and I. Hallikia, The Aus IMM 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).

Time (t) 4 8 16 30 60 120 Percent extracted (y) 1.2 1.6 2.3 2.8 3.6 4.4

a. The article suggests fitting a quadratic model y = ????0 + ????1t + ????2t 2 + ???? 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 = ????1 + 2????2t. Estimate the time at which the reaction rate will be equal to 0.05.

c. The reaction rate at t = 0 is equal to ????1. 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.