To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t) of rats alive at time t (in months) satisfies the Gompertz differential equation

Exercise 0.2.12: Is there a solution to y' = y, such that y(0) = y(1)? Exercise 0.2.13: The population of city X was 100 thousand 20 years ago, and the population of city X was 120 thousand 10 years ago. Assuming constant growth, you can use the exponential population model (like for the bacteria). What do you estimate the population is now?

Suppose the population of a species of animals on an island is governed by the logistic model with relative rate of growth k = 0.05 and carrying capacity M= 15000. I.e., the population function P(t) satisfies the equation P' = bP(15000 - P), where b = k/M. If the current population is P(0) = 20000, which one of the following is closest to P(1)? O a) 19700 O b) 19890 Oc) 19680 Od) 19690 Oe) 19805 Of) 19742 Motion

Differential equations have been used extensively in the study of drug dissolution for patients given oral medications. The three simplest equations used are the zero-order kinetic equation, the Noyes-Whitney equation, and the Weibull equation. All assume that the initial concentration is zero but make different assumptions about how the concentration increases over time during the dissolution of the medication. The zero-order kinetic equation states that the rate of change in the concentration of drug c (in mg/mL) during dissolution is governed by the differential equation dc dt = k where k is a positive constant. Is this differential equation pure-time, autonomous, or nonautonomous? pure time autonomous nonautonomous State in words what this differential equation says about how drug dissolution occurs. The drug concentration increases linearly with time during dissolution. The drug concentration remains constant with time during dissolution. The drug concentration…