MATH 37Lecture Guide UNIT 2 albabierra14(Population studies)In many population growth models, there is an upper limit beyond which thepopulation cannot grow. Let us suppose that the earth will not support a population of more than 16billion and that there were 2 billion people in 1925 and 4 billion in 1975. Then ifyis the populationtyears after 1925, an appropriate model is the differential equationykydtdy16. (i.) Solve fory(as a function oft). (ii.) Find the population in 2015. (iii.) When will the population be 9 billion?__________________________2.5 Other Substitution Techniques(TC7 pp. 614-619 / TCWAG pp. 566-569)For rational functions of sine and cosine,use the substitute:21tanzcos,sin,dExercise Items.Evaluate the following using a proper substitute.1.dcoscos535.23cosd2.35sind6.tansind3.cossind347.dcossin224.cossind18.dsintan21Must try!!!cossindTO DO!!!Evaluate the following by using proper substitutes.1.2cossind2.tansind