Calculus: An Applied Approach (MindTap Course List)
10th Edition
ISBN: 9781305860919
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 11.4, Problem 17E
To determine
The population of the city in the year 2025 if the population was 200,000 in 2010 year and the proportional constant was 0.015.
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Check out a sample textbook solutionChapter 11 Solutions
Calculus: An Applied Approach (MindTap Course List)
Ch. 11.1 - Checkpoint 1 Worked-out solution available at...Ch. 11.1 - Prob. 2CPCh. 11.1 - Prob. 3CPCh. 11.1 - Prob. 4CPCh. 11.1 - Prob. 1SWUCh. 11.1 - Prob. 2SWUCh. 11.1 - Prob. 3SWUCh. 11.1 - Prob. 4SWUCh. 11.1 - Prob. 5SWUCh. 11.1 - Prob. 6SWU
Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Verifying Solutions In Exercises 1-12, verify the...Ch. 11.1 - Prob. 10ECh. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Prob. 16ECh. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Investment The rate of growth of an investment is...Ch. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.2 - Checkpoint 1 Worked-out solution available at...Ch. 11.2 - Prob. 2CPCh. 11.2 - Prob. 3CPCh. 11.2 - Prob. 4CPCh. 11.2 - Prob. 5CPCh. 11.2 - Prob. 6CPCh. 11.2 - Prob. 1SWUCh. 11.2 - Prob. 2SWUCh. 11.2 - Prob. 3SWUCh. 11.2 - Prob. 4SWUCh. 11.2 - Prob. 5SWUCh. 11.2 - Prob. 6SWUCh. 11.2 - Prob. 7SWUCh. 11.2 - Prob. 8SWUCh. 11.2 - Prob. 9SWUCh. 11.2 - Prob. 10SWUCh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 33ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 35ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Solve the differential equation. Weight Gain A...Ch. 11.2 - Prob. 1QYCh. 11.2 - Prob. 2QYCh. 11.2 - Prob. 3QYCh. 11.2 - Prob. 4QYCh. 11.2 - Prob. 5QYCh. 11.2 - Prob. 6QYCh. 11.2 - Prob. 7QYCh. 11.2 - Prob. 8QYCh. 11.2 - Prob. 9QYCh. 11.2 - Prob. 10QYCh. 11.2 - Prob. 11QYCh. 11.2 - Prob. 12QYCh. 11.2 - Prob. 13QYCh. 11.2 - Prob. 14QYCh. 11.2 - Prob. 15QYCh. 11.2 - Ignoring resistance, a sailboat starting from rest...Ch. 11.3 - Checkpoint 1 Worked-out solution available at...Ch. 11.3 - Prob. 2CPCh. 11.3 - Prob. 3CPCh. 11.3 - Prob. 1SWUCh. 11.3 - Prob. 2SWUCh. 11.3 - Prob. 3SWUCh. 11.3 - Prob. 4SWUCh. 11.3 - Prob. 5SWUCh. 11.3 - Prob. 6SWUCh. 11.3 - Prob. 7SWUCh. 11.3 - Prob. 8SWUCh. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - Prob. 10SWUCh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 10ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 17ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Vertical Motion A falling object encounters air...Ch. 11.3 - Velocity A booster rocket carrying an observation...Ch. 11.3 - Learning Curve The management at a medical supply...Ch. 11.3 - Investment Let A he the amount in a fund earning...Ch. 11.4 - Prob. 1CPCh. 11.4 - Prob. 2CPCh. 11.4 - Checkpoint 3 Worked-out solution available at...Ch. 11.4 - Prob. 4CPCh. 11.4 - Checkpoint 5 Worked-out solution available at...Ch. 11.4 - Prob. 1SWUCh. 11.4 - Prob. 2SWUCh. 11.4 - Prob. 3SWUCh. 11.4 - Prob. 4SWUCh. 11.4 - Prob. 5SWUCh. 11.4 - Prob. 6SWUCh. 11.4 - Prob. 7SWUCh. 11.4 - Prob. 8SWUCh. 11.4 - Prob. 9SWUCh. 11.4 - Prob. 10SWUCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Advertising Awareness In Exercises 3 and 4, use...Ch. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Chemistry A wet towel hung from a clothesline to...Ch. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Biology A population of eight beavers has been...Ch. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Chemical Mixture A 100-gallon tank is full of a...Ch. 11.4 - Chemical Mixture A 200-gallon tank is half full of...Ch. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Finding a Particular Solution In Exercises 15 and...Ch. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Prob. 47RECh. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Prob. 55RECh. 11 - Prob. 56RECh. 11 - Solving a Linear Differential Equation In...Ch. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - Prob. 60RECh. 11 - Prob. 61RECh. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Prob. 64RECh. 11 - Prob. 65RECh. 11 - Prob. 66RECh. 11 - Safety Assume the rate of change per hour in the...Ch. 11 - Prob. 68RECh. 11 - Prob. 69RECh. 11 - Prob. 70RECh. 11 - Prob. 71RECh. 11 - Prob. 72RECh. 11 - Prob. 73RECh. 11 - Prob. 74RECh. 11 - Prob. 75RECh. 11 - Chemical Mixture A tank contains 30 gallons of a...Ch. 11 - Chemical Mixture A tank contains 20 gallons of a...Ch. 11 - Prob. 1TYSCh. 11 - Prob. 2TYSCh. 11 - Prob. 3TYSCh. 11 - Prob. 4TYSCh. 11 - Prob. 5TYSCh. 11 - Prob. 6TYSCh. 11 - Prob. 7TYSCh. 11 - Prob. 8TYSCh. 11 - Prob. 9TYSCh. 11 - Prob. 10TYSCh. 11 - Prob. 11TYSCh. 11 - A lamb that weighs 10 pounds at birth gains weight...Ch. 11 - Prob. 13TYS
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- Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.arrow_forwardDecay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forwardKeplers Third Law Keplers Third Law of planetary motion states that the square of the period T of a planet the time it takes for the planet to make a complete revolution about the sun is directly proportional to the cube of its average distance d from the sun. a Express Keplers Third Law as an equation. b Find the constant of proportionality by using the fact that for our planet the period is about 365 days and the average distance is about 93 million miles. c The planet Neptune is about 2.79109 mi from the sun. Find the period of Neptune.arrow_forward
- Hubbles Constant Astronomers believe that the universe is expanding and that stellar objects are moving away from us at a radial velocity V proportional to the distance D from Earth to the object. a. Write V as a function of D using H as the constant of proportionality. b. The equation in part a was first discovered by Edwin Hubble in 1929 and is known as Hubbles law. The constant of proportionality H is known as Hubbles constant. The currently accepted value of Hubbles constant is 70 kilometers per second per megaparsec. One megaparsec is about 3.0861019 kilometers. With these units for H, the distance D is measured in megaparsecs, and the velocity V is measured in kilometers per second. The galaxy G2237+305 is about 122.7 megaparsecs from Earth. How fast is G2237+305 receding from Earth? c. One important feature of Hubbles constant is that scientists use it to estimate the age of the universe. The approximate relation is y=1012H Where y is time in years. Hubbles constant is extremely difficult to measure, and Edwin Hubbles best estimate in 1929 was about 530 kilometers per second per megaparsec. What is the approximate age of the universe when this value of H is used? d. The calculation in part c would give scientists some concern, since Earth is thought to be about 4.6 billion years old. What estimate of the age of the universe does the more modern value of 70 kilometers per second per megaparsec give?arrow_forwardHookes Law Hookes Law states that the force needed to keep a spring stretched x units beyond its natural length is directly proportional to x. Here the constant of proportionality is called the spring constant. a Write Hookes Law as an equation. b If a spring has a natural length of 5 cm and a force of 30 N is required to maintain the spring stretched to a length of 9 cm, find the spring constant. c What force is needed to keep the spring stretched to a length of 11 cm?arrow_forward
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