2. If one denotes the population of a planet by E(t) per year t, then the population growth rate dE/dt is characterized by dE dt = kE, where k denotes the constant of proportionality. (a) Find an exact expression for k given that the population E of the planet doubles every 37 years. (b) The population of this city is initially 300, 000. How many years (T) would it take for the population to grow to 10, 000, 000? Give your answer to the nearest year.

The half life of substance A is 22 years, and substance B decays at a rate of 30 each decade. (a) Find a formula for a function f(t) that gives the amount of substance A, in milligrams, left after t years, given that the initial quantity was 100 milligrams. f(t) = help (formulas) (a) Find a formula for a function g(t) that gives the amount of substance B, in milligrams, left after t years, given that the initial quantity was 100 milligrams. g(t) help (formulas) (c) of which substance is there less in the long term? OA. There is less of substance B in the long term. OB. There is less of substance A in the long term. OC. There is no way to tell.