INSTRUCTIONS: On a separate sheet of paper, write out the solutions to the following problems. Show all steps in the solution and use complete sentences when asked to give interpretations of your answers. Show all steps. If a graph does not have correct axes labeled, scale labeled, or graphs labeled it will not receive full credit. You may use calculators to check your work, but you are being graded on your algebraic work. No credit will be given to just a nal answer without supporting work. If you use outside resources (including your peers and chegg) make sure you cite them at the top of the page and put the answers in your own words with proper justication. 1. Solve the differential equation given that y = 0 when :1: = 0. (Note: technically there are innitely many values of C that can satisfy this equation, but you just need to ne one) 2. Suppose y(t) represents the population of Pima County (in millions of people) t years after 1980. Its growth is modeled by the differential equation dy = 0.15 2 dt y( y) (a) Solve the differentiable equation (this will require partial fractions). Include C as your arbitrary constant. Clean up your answer as much as possible. (there is a lot of algebra here, so show all your work!) (b) Determine the value of C so that in 1980 the population was y = 0.5 (that means 500,000 people). (0) Using your model, what was the population in 2019? Compare this to the actual value of 1.04 million