The rate at which a drug leaves the bloodstream and passes into the urine is

Find solutions to the differential equations in Problems 16, subject to the given initial condition. dP dt = 0.02P, P(0) = 20

Find solutions to the differential equations in Problems 16, subject to the given initial condition. dw dr = 3w, w = 30 when r = 0

Find solutions to the differential equations in Problems 16, subject to the given initial condition. dy dx = 0.14y, y = 5.6 when x = 0

Find solutions to the differential equations in Problems 16, subject to the given initial condition. dQ dt = Q 5 , Q = 50 when t = 0

Find solutions to the differential equations in Problems 16, subject to the given initial condition. dp dq = 0.1p, p = 100 when q = 5

Find solutions to the differential equations in Problems 16, subject to the given initial condition. dy dx + y 3 = 0, y(0) = 10

A deposit of $5000 is made to a bank account paying 1.5% annual interest, compounded continuously. (a) Write a differential equation for the balance in the account, B, as a function of time, t, in years. (b) Solve the differential equation. (c) How much money is in the account in 10 years?

Money in a bank account grows continuously at an annual rate of r (when the interest rate is 5%, r = 0.05, and so on). Suppose $2000 is put into the account in 2010. (a) Write a differential equation satisfied by M, the amount of money in the account at time t, measured in years since 2010. (b) Solve the differential equation. (c) Sketch the solution until the year 2040 for interest rates of 5% and 10%.

Abank account that earns 10%interest compounded continuously has an initial balance of zero. Money is deposited into the account at a continuous rate of $1000 per year. (a) Write a differential equation that describes the rate of change of the balance B = f(t). (b) Solve the differential equation.

The amount of ozone, Q, in the atmosphere is decreasing at a rate proportional to the amount of ozone present. If time t is measured in years, the constant of proportionality is 0.0025. Write a differential equation for Q as a function of t, and give the general solution for the differential equation. If this rate continues, approximately what percent of the ozone in the atmosphere now will decay in the next 20 years?

Using the model in the text and the data in Table 9.6 on page 427, find how long it would take for 90% of the pollution to be removed from Lake Michigan and from Lake Ontario, assuming no new pollutants are added. Explain how you can tell which lake will take longer to be purified just by looking at the data in the table.

Use the model in the text and the data in Table 9.6 on page 427 to determine which of the Great Lakes would require the longest time and which would require the shortest time for 80% of the pollution to be removed, assuming no new pollutants are being added. Find the ratio of these two times.

The rate at which a drug leaves the bloodstream and passes into the urine is proportional to the quantity of the drug in the blood at that time. If an initial dose of Q0 is injected directly into the blood, 20% is left in the blood after 3 hours. (a) Write and solve a differential equation for the quantity, Q, of the drug in the blood after t hours. (b) How much of this drug is in a patients body after 6 hours if the patient is given 100 mg initially?

In some chemical reactions, the rate at which the amount of a substance changes with time is proportional to the amount present. For example, this is the case as - glucono-lactone changes into gluconic acid. (a) Write a differential equation satisfied by y, the quantity of -glucono-lactone present at time t. (b) If 100 grams of -glucono-lactone is reduced to 54.9 grams in one hour, how many grams will remain after 10 hours?

Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 1 million barrels of oil in the well; six years later 500,000 barrels remain. (a) At what rate was the amount of oil in the well decreasing when there were 600,000 barrels remaining? (b) When will there be 50,000 barrels remaining?

Hydrocodone bitartrate is used as a cough suppressant. After the drug is fully absorbed, the quantity of drug in the body decreases at a rate proportional to the amount left in the body. The half-life of hydrocodone bitartrate in the body is 3.8 hours and the dose is 10 mg. (a) Write a differential equation for the quantity, Q, of hydrocodone bitartrate in the body at time t, in hours since the drug was fully absorbed. (b) Solve the differential equation given in part (a). (c) Use the half-life to find the constant of proportionality, k. (d) How much of the 10-mg dose is still in the body after 12 hours?

The amount of land in use for growing crops increases as the worlds population increases. Suppose A(t) represents the total number of hectares of land in use in year t. (A hectare is about 21 2 acres.) (a) Explain why it is plausible that A(t) satisfies the equation A(t) = kA(t). What assumptions are you making about the worlds population and its relation to the amount of land used? (b) In 1966 about 4.55 billion hectares of land were in use; in 1996 the figure was 4.93 billion hectares.2 If the total amount of land available for growing crops is thought to be 6 billion hectares, when does this model predict it will be exhausted? (Let t = 0 in 1966.)