Growth Problems Applications of Differential Equations: Growth Problems. Suppose a population of insect increases at a rate proportional to the amount present. There were 100 insects after the third day of the experiment and 250 insects after the seventh day. Approximately how many insects were in the original population? How many insects will there be after 24 days? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial Conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the population at t=0 and t= 24 7. Graph the equation Assessment: 7 of 10 Tests Passed (70%) The Differential Equation Model Is the model for condition 1 properly set? Variable k1 must be of data type sym. It is currently of type symfun. Check where the variable is assigned a value. Is the model for condition 1 properly set? Variable k2 must be of data type sym. It is currently of type symfun. Check where the variable is assigned a value. The growth rate constant factor Variable k has an incorrect value. The decimal value of Initial Population The General Model The initial Population The Population at 24 days Functions Used My Solutions > The Final Population Submit ? 10% (10%) 0% (10%) 0% (10%) 0% (10%) 10% (10%) 10% (10%) 10% (10%) 10% (10%) 10% (10%) 10% (10%)
Growth Problems Applications of Differential Equations: Growth Problems. Suppose a population of insect increases at a rate proportional to the amount present. There were 100 insects after the third day of the experiment and 250 insects after the seventh day. Approximately how many insects were in the original population? How many insects will there be after 24 days? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial Conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the population at t=0 and t= 24 7. Graph the equation Assessment: 7 of 10 Tests Passed (70%) The Differential Equation Model Is the model for condition 1 properly set? Variable k1 must be of data type sym. It is currently of type symfun. Check where the variable is assigned a value. Is the model for condition 1 properly set? Variable k2 must be of data type sym. It is currently of type symfun. Check where the variable is assigned a value. The growth rate constant factor Variable k has an incorrect value. The decimal value of Initial Population The General Model The initial Population The Population at 24 days Functions Used My Solutions > The Final Population Submit ? 10% (10%) 0% (10%) 0% (10%) 0% (10%) 10% (10%) 10% (10%) 10% (10%) 10% (10%) 10% (10%) 10% (10%)
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:Growth Problems
Applications of Differential Equations: Growth Problems
Suppose a population of insect increases at a rate proportional to the amount present.
There were 100 insects after the third day of the experiment and 250 insects after the seventh day.
Approximately how many insects were in the original population? How many insects will there be after 24 days?
Solve the equation via MATLAB making sure that you passed though the following:
1. Initialization of variables
2. Setting up the differential equations
3. Listing down initial Conditions
4. Solving for the parameter k.
5. Finding the resulting model
6. Finding the population at t=0 and t= 24
7. Graph the equation
Assessment: 7 of 10 Tests Passed (70%)
The Differential Equation Model
Is the model for condition 1 properly set?
Variable k1 must be of data type sym. It is currently of type symfun. Check where the variable is assigned a value.
Is the model for condition 1 properly set?
Variable k2 must be of data type sym. It is currently of type symfun. Check where the variable is assigned a value.
The growth rate constant factor
Variable k has an incorrect value.
The decimal value of Initial Population
The General Model
The initial Population
The Population at 24 days
Functions Used
My Solutions >
The Final Population
Submit
10% (10%)
0% (10%)
0% (10%)
0% (10%)
10% (10%)
10% (10%)
10% (10%)
10% (10%)
10% (10%)
10% (10%)
Total: 70%
Transcribed Image Text:Script
1 % Suppose a population of
insect increases at a rate proportional to the amount present.
after the third day of the experiment and 250 insects after the seventh day.
2 % There were 100 insects
3% Approximately how many insects were in the original population? How many insects will there be after 24 days?
8
9
4
5 %Setup the variables P(t), k that will be used in the program. Find also the derivative of P(t) and set as dp
6 syms P(t) kt;
7 dp = diff (P);
10
11 %Initial Conditions
12 cond1=P(3) == 100;
13 cond2=P(7) == 250;
14
15 %Set the differential equation model as eqn1;
16 eqn1 = dp==k*P;
17
18
19 %Find k1 and k2, by solving the initial value problem eqnl using condl and cond2, respectively.
20 k1(t, k)=dsolve (eqn1, cond1);
21 k2(t, k)=dsolve (eqn1, cond2);
22
23 % Solve for k by equating k1 and k2 at t-0. Save results as k.
24 Sol1(k)= k1(0,k)-k2(0,k)
25 Res1-solve(Sol1(k));
Save
26 % Solve the eqn1 using the acquired value of k and using Initial value cond1.
27 fprintf('Value of k is \n');
28 disp(Resl)
29 %Evaluate Psoln at t=0, save your answer as P0. Express your answer in decimals, save answer as Po.
30 Psoln(t) = k1(t, Res1);
31 x = linspace(-1,25,100);
32 y Psoln(x);
33 PO Psoln(0);
34 Po double (PO)
35 %Evaluate Psoln at t=24, save your answer as P24. Express your answer in decimals, save answer as Po24.
36 P24 Psoln (24);
37 Po24 double (P24);
38 %Graphing of Output (Take note of the Code)
39 Title "Growth Problem";
40 XValue= "Days";
41 YValue = "Number of Insects";
42 plot (x, y, 'b--');
43 hold on;
44 title (Title);
45 xlabel (XValue);
46 ylabel (YValue);
47 plot (0, Psoln (0), '*');
C Reset
48 plot (24, Psoln (24), '*');
49 hold off;
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