{Use of Tech} Intravenous drug dosing The amount of drug in the blood of a patient (in milligrams) administered via an intravenous line is governed by the initial value problem y’(t) = -0.02y + 3, y(0) = 0 where t is measured in hours.


b. What is the steady-state level of the drug?

Case 2 of the general solution Solve the equation y′(t) = ky + b in the case that ky + b < 0 and verify that the general solution is y(t) = Ceᵏᵗ − b/k.

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample

b. If k>0 and b>0 then y(t)=0 is never a solution of y'(t)=ky−b.

{Use of Tech} Endowment model An endowment is an investment account in which the balance ideally remains constant and withdrawals are made on the interest earned by the account. Such an account may be modeled by the initial value problem B′(t)=rB−m, for t≥0, with B(0)=B0. The constant r>0 reflects the annual interest rate, m>0 is the annual rate of withdrawal, B0 is the initial balance in the account, and t is measured in years.

a. Solve the initial value problem with r=0.05, m=\$1000/year, and B0=\$15,000 Does the balance in the account increase or decrease?

{Use of Tech} Fish harvesting A fish hatchery has 500 fish at t=0, when harvesting begins at a rate of b>0fish/year The fish population is modeled by the initial value problem y′(t)=0.01y−b,y(0)=500 where t is measured in years.

c. Graph the solution in the case that b=60fish/year. Describe the solution.

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample

d. According to Newton’s Law of Cooling, the temperature of a hot object will reach the ambient temperature after a finite amount of time.