Write and find the general solution of the differential equation that models the verbal statement. The rate of change of N is proportional to N. (Use k for the proportionality constant.) dN dt = kN   N(t) = Cc4t   Evaluate the solution at the specified value of the independent variable. When t = 0, N = 150, and when t = 1, N = 200. What is the value of N when t = 4?

A virus spreads by contact and if you get infected you stay contagious. In an isolated population with P persons (no-one dies or are born) the rate of infection at time t (in months after 1/1 2020) is proportional to the product of 1. the number y(t) that are infected, 2. the number that are not infected 3. eat where a is a negative number depending on disease preventive measures. One tenth of the population is infected 1/1-2020. (a) Write out the differential equation y(t) must satisfy and solve it (call the proportionality constant k and remember to explain each step of your solution carefully. Are there for instance any constant solutions?). (b) Find a relation between L = lim->00 y(t), a, Pand k. What can you say about L when a is very small? What can you say about L when a is very big?

dT dt Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is = K[M(t)- T(t)], where K is a constant. Let K = 0.04 (min) temperature of the medium be constant, M(t) = 291 kelvins. If the body is initially at 365 kelvins, use Euler's method with h = 0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes. (a) The temperature of the body after 30 minutes is kelvins. (Round to two decimal places as needed.) (...) and the

dC The rate of change in the concentration of a drug with respect to time in a user's blood is given by = - kC + D(t), where D(t) is dosage at time t and k is the rate that the drug leaves the bloodstream. Complete dt parts (a) and (b) below. t (a) Solve this linear equation to show that, if C(0) = 0, then C(t) = e -kt ,ky D(y)dy. dC dy Begin by writing the differential equation, = - kC + D(t), in the form dt + P(x)y = Q(x). dx dC + %3D dt

Water flows into a tank, and a certain part of it drains out through a valve. The volume v (in cubic feet) of water in the tank at time t satisfies the equation dv/dt = 5 − (v/3). If the process continues for a long time, how much water will be in the tank?a. 13 cubic feetb. 14 cubic feetc. 15 cubic feetd. 16 cubic feet