The amount, A mg, of caffeine in the body it hours after drinking a cup of coffee can be approximated by A = f (t) = 150601\". (a) Find f'(t) m: :] (b) Find f(2) and f'(2) and give units. NOTE: Round your answers to two decimal places. f=- f'(2)=- The population of Hungary1 has been modeled by P = 9.919(0998)', where P is in millions and t is in years since July 2014. Assume the trend continues. (a) What does this model predict for the population of Hungary in July 2025? Round your answer to two decimal places. This model predicts the population in July 2025 is I I million. (b) How fast (in people/year) does this model predict Hungary's population will be decreasing in 2025? Give your answer to the nearest hundred. This model predicts that in 2025, Hungary's population will be decreasing by n I people per year. The temperature, H , in degrees Fahrenheit (OF)7 of a can of soda that is put into a refrigerator to cool is given as a function of time, t, in hours, by H = 42 + 328375. (a) Find the rate at which the temperature of the soda is changing. dt_ / our dH (b) What is the sign of E ? The sign of (iiI: is dH (0) When, for t Z 0, is the magnitude of largest? dt t= A country's production of solar power, in megawatts, can be modeled byf(t) = 570(11)' ,where r is years since 2000. Findf(0),f' (O), f(20), andf'(20). Give units and interpret your answers in terms of solar power. Round your answers to the nearest integer. In 2000, solar power production was I: megawatts and production was increasing at a: megawatts per year. In I , solar power production will be a: megawatts and production will be increasing at about u megawatts per year. \fDifferentiate the function. R(q) = 2In q R' ( q) =