Exam 16: Methods and Applications of Integration

The population of a certain city was 1,500,000 in the year 1580.The population grew by 5% each year of the next 15 years.The population declined by 10% each year for the rest of the century.What was the population of the city in the year 1600?

Determine if converges or diverges.If it converges,to what number does it converge?

Use the tables to find: dx

Either find the value of or show that it diverges.

Find y if = and y(1)= 10,x > 0,y > 0.

The number of weekly sales of a product was found to be given by S(t)= 100 + 100,where t is the number of days after the start of advertising on the radio.Find the average weekly sales during the first 10 weeks of the advertising.

Use the table below to determine Indicate the formula number employed. I. + C II. + C III. + C IV. + C

Suppose the points (0,2),(1,3)and (2,0)lie on the graph of the continuous function f.Using the trapezoidal rule and all of these points,an approximation to is

Find the present value of a continuous annuity at an annual rate of 9% for five years if the payment at time t is at the annual rate of f(t)= 3000 dollars.Express your answer in terms of e.

Suppose 40% of a radioactive substance remains after 2 years.Assume that ln 0.4 = -0.9 and find the decay constant.

The growth rate of a cell satisfies = k ,where t is the time in months,V is the volume in cubic millimeters,and k is a constant.If V = 0 when t = 0,find V as a function of t.

Find the exact area of the region bounded by y = f(x)= + x,x = 0,x = 2,and the x-axis.

An ecologist has determined that a local metro-park has food to support up to 200 rabbits at any given time.Now,from observations,he estimates that there are 20 rabbits.One week from now,he estimates that there are 30 rabbits.Assuming logistic growth,find the logistic function that will model this rabbit population.

Solve the differential equation: = ,y > 0

The exact area of the region bounded by the graphs of y = x,y = ,y = 2,and y = 3 is

In a city whose population is 30,000,an outbreak of flu occurs.A researcher studying the spread of the flu determines from the surrounding hospitals and the health department that there where 600 infected persons one week ago.This week there are 1,000 infected persons.Assuming logistic growth,estimate the number of infected people 3 weeks from now.

Find the average value of the function y = f(x)= + 1 on the interval .Use your graphing calculator to graph both y = f(x)= + 1 and y = on the same set of axes.Estimate the value of x when these two curves intersect.

The average value of f(x)= over the interval Is

Find the average value of the function f(x)= 2x + 3 over the interval .

Find the exact area of the region bounded by y = f(x)= ,x = -2,x = 2,and the x-axis.