1) Find a solution of the differential equation: dy =1.6y, where y = 18 when t = 0. dt Hint: look on page 1 of the lecture notes. There are not very many steps to this problem.2) A radioactive substance has half-life 28.9 hours. You start with 1.442 micrograms. a) Find an exponential model. b) How much remains after 39.4 hours? c) How long until 0.100 micrograms remain? d) What is the rate of decay at the 12-hour mark?3) The population of a city is 32,000 in 1980 and doubles every 15 years. a) Find an exponential model. b) What is the population in 2021? c) In what year will population be 140,000? d) What is the rate of population growth in 1990?4) Consider f(t) = 10e-0.6 + 18 a) What is /(0)? b) What is lim f(t)? c) Make a graph of y = {{r)