mathematically as dy dt' = ay dt Population growth is commonly modeled upon the simple statement that the popu- dy lation growth rate, d, is proportional to the present population, y. This can be written where a > 0. You have just purchased a piece of property with a small lake that is suitable for raising trout. You feel that without any aid from you the trout population introduced into the pond will grow at a nominal annual rate of 5%. You realize the resulting D.E. for the growth rate becomes = (1/20) y. 1. = dt draw the slope field for the D.E., dy y. Also, plot a solution graph through the point that would correspond to the introduction of 50 trout (hopefully with both sexes) into the pond today, t = 0. Remember you will need to import this into your Mini-Project document. 2. State an explicit solution to the D.E., = y with y(0) = 50. 3. Use the explicit solution to find the projected undisturbed trout population in the lake after 10 yrs, 30 yrs, 50 yrs, and 70 yrs. Give approximations to 2 decimal places.