When U.S. energy use per dollar of GDP is indexed to 1980, that energy use for any year is viewed as a percent of the use per dollar of GDP in 1980. By using U.S. Department of Energy data for selected years from 1985 and projected to 2035, energy use per dollar of GDP can be modeled by the function
E(t)= 96e-0.019t
where t is the number of years past 1980.
(a) Find the function that describes how rapidly the energy use per dollar of GDP is changing.
(b) Find and interpret E(50) and E`(50).