An urban area is considering repaving 1000 km of asphalt roads with concrete pavement. They want to combat the "urban heat island effect" in order to reduce the greenhouse gas (GHG) emissions from building energy demand (BED). To do this, they are going to raise the albedo (basically, how much it reflects sunlight) of the new pavement by adding ground granulated blast furnace slag (GGBFS) to the concrete.

Let A(s) be the albedo of concrete made with a GGBFS composition of s percent. Albedo is a quantity ranging from 0 to 1.

Let G(a) represent the 50-year BED GHG emissions reduction from replacing the asphalt pave- ment with the new concrete pavement having albedo a. The units of G are billions of kilograms CO2-equivalent. Assume that both of these functions are differentiable and invertible.

1. Give separate (different) explanations of what the derivatives de and . [G(A(s))] measure.

2. Here we investigate an application of the formula (G^-1)(0.5) = 2.

(a) Represent the quantity "The albedo of concrete that will save 500 million kilograms of emissions" using a formula.

(b) You are given the fact that (G^-1)(0.5) = 2. Use the linear approximation of G to estimate the change in albedo required to go from saving 500 million kilograms of emission to saving 600 million kilograms of emission.