Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
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Chapter 3.2, Problem 15E
To determine
To find:
Population of alligators in the year
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. A contagious disease is spreading in a town of 10,000 people. There were 200 infectedpeople when the outbreak was discovered, and the number grew up to 1,000 after one month.Assuming the logistic model for the spread of the disease, find the number of infected peoplethree months after the outbreak.
Suppose that a population follows a logistic growth model. The population in the first year is 21.7 thousand. In the second year the population has increased by 54 hundred. In the third year, the population has increased by 17 hundred.
Find the carrying capacity of the population.
(1) Confirm that the data in Table 1.2 for the temperatures 25 °C and 45 °C can
also be approximated by constant relative changes. Then find the exponentials
that match the data.
Chapter 3 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - A swimming pool whose volume is 10,000gal contains...Ch. 3.2 - The air in a small room 12ft by 8ft by 8ft is 3...Ch. 3.2 - Beginning at time t=0, fresh water is pumped at...Ch. 3.2 - A tank initially contains S0lb of salt dissolved...Ch. 3.2 - In 1990 the Department of Natural Resources...Ch. 3.2 - Prob. 10E
Ch. 3.2 - Prob. 11ECh. 3.2 - For the logistic curve15, assume pa:=p(ta) and...Ch. 3.2 - In Problem 9, suppose we have the additional...Ch. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - 16 Show that for a differentiable function p(t),...Ch. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - A snowball melts in such a way that the rate of...Ch. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Early Monday morning, the temperature in the...Ch. 3.3 - During the summer the temperature inside a van...Ch. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 7ECh. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 9ECh. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - In Problem 16, let I=50 kg-m2 and the retarding...Ch. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Rocket Flight. A model rocket having initial mass...Ch. 3.4 - Escape Velocity. According to Newtons law of...Ch. 3.5 - An RL circuit with a 5- resistor and a 0.05-H...Ch. 3.5 - Prob. 2ECh. 3.5 - The pathway for a binary electrical signal between...Ch. 3.5 - If the resistance in the RL circuit of Figure...Ch. 3.5 - Prob. 5ECh. 3.5 - 6. Derive a power balance equation for the RL and...Ch. 3.5 - 7. An industrial electromagnet can be modeled as...Ch. 3.5 - 8. A 108F capacitor 10 nanofarads is charged to 50...Ch. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - In Example 1, page 126, the improved Eulers method...Ch. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Use the improved Eulers method subroutine with...Ch. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Use the improved Eulers method with tolerance to...Ch. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - The solution to the initial value problem...Ch. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 20ECh. 3.7 - Determine the recursive formulas for the Taylor...Ch. 3.7 - Determine the recursive formulas for the Taylor...Ch. 3.7 - Prob. 3ECh. 3.7 - Prob. 4ECh. 3.7 - Prob. 5ECh. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - Prob. 10ECh. 3.7 - Prob. 11ECh. 3.7 - Prob. 12ECh. 3.7 - Prob. 13ECh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - The Taylor method of order 2 can be used to...Ch. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Prob. 20ECh. 3.7 - Prob. 21E
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- What might a scatterplot of data points look like if it were best described by a logarithmic model?arrow_forwardTo the nearest whole number, what is the initial value of a population modeled by the logistic equation P(t)=1751+6.995e0.68t ? What is the carrying capacity?arrow_forwardDoes a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.arrow_forward
- An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?arrow_forwardWith what kind of exponential model would doubling time be associated? What role does doubling time play in these models?arrow_forwardUse a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?arrow_forward
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