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A tumor may be regarded as a population of multiplying cells. It is found empirically that the “birth rate” of the cells in a tumor decreases exponentially with time, so that
Solve this initial value problem for
Observe that P (t ) approaches the finite limiting population
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Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
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- Q1/ The ideal gas equation of state is given by: PV = nRT Where: P is the pressure (atm), V is the volume (L), T is the temperature (K), R=0.08206 (L atm)/(mol K) is the gas constant, and n is the number of moles. Real gases, especially at high pressures, deviate from this behavior. Their responses can be modeled with the van der Waals equation: P-- nRT n² a + = 0 V-nb V2 Where a and b are material constants. For CO₂ a 3.5924 L'atm/mol², and b=0.04267 L/mol. Calculate P from both equations for CO₂ gas with 40 values of V between 0.01 and 1.5 and display the results in: 1- Three-column table where the values of Vand both P are displayed in the first, second, and third columns, respectively. 2-Plot V versus both P in two different plots in the same figure with a solid line, black color, with circle marker. Add a title, labels, and the grid to the plot. Make all texts bold with font size of 13. Take T-298K and n-3 moles.arrow_forwardWhen purifying drinking water you can use a so-called membrane filtration. In an experiment one wishes to examine the relationship between the drop across a membrane and the flux (flow per area) through the membrane. We observe the following 10 related values of pressure (x) and flux (y): pressure 2 3 4 5 6 7 8 9. 10 Pressure (x) 1.02 2.08 2.89 4.01 5.32 5.83 7.26 7.96 9.11 9.99 Flux (y) 1.15 0.85 1.56 1.72 4.32 5.07 5.00 5.31 6.17 7.04 Copy this into R to avoid typing in the data: D <- data.frame( pressure=c(1.02,2.08,2.89,4.01,5.32,5.83,7.26,7.96,9.11,9.99), flux=c(1.15,0.85,1.56,1.72,4.32,5.07,5.00,5.31,6.17,7.04)arrow_forwardSolve the following: (1) g(x) = tan(x³), find g(x); (2) h(x) = (sin(3x))/2x, find h"(x); (3) m(x) = In(Tan-¹x), find m'(x) (4) Find Dy(x) given y(x), if Dy(x) = y(x) (5) Find D2y(x) given y(x), if D2y(x) = y"(x) Script 1% Initialize the variable and the functions 2 3 %Set your g(x) ad h(x) and m(x) 4 g(x) = 5 h(x) = 6 m(x) = 7% Find the derivative of g(x). save answer as gp(x); 8 gp(x) = 9% Find the second derivative of h(x). save answer as hpp(x); 10 hpp(x) = 11 % Find the derivative of m(x). save answer as mp(x); 12 mp(x) = 13 % Find the derivative of y and 14 Dy(x)= 15 % Find the derivative of y and set it as D2y(x) 16 D2y(x)= Assessment: Functions Functions Used Declaration Declaration Declaration Solving Solving Solving Solving Solving set it as Dy(x) Save C Reset MATLAB Documentation ▶ Run Script ? Submit ? ?arrow_forward
- An oscillating current in an electric circuit is described by i(t) = 9e cos(2rt) where t is in seconds. Use False Position Method to determine the value of t such that i=3.5. Plot the graph of the function to develop your initial guess. Terminate your computation when the approximate relative error falls below ɛs=10°. Give the results in a table.arrow_forwardSolve it , only if you are really very very good in it. Otherwise i will downvote. Computer sciencearrow_forwardI need the answer as soon as possible Q4/ The ideal gas equation of states is given by: PV = nRT Where: P is the pressure, V is the volume, T is the temperature, R=0.08206 (L atm)/(mol K) is the ideal gas constant, and n is the number of moles. Real gases, especially at high pressures, deviate from this behavior. Their responses can be modeled with the van der Waals equation: nRT using matlab V-nb + n² a V² Where a and b are gas constants. For Cl₂ a = 6.579 L'atm/mol², and b = 0.0562 L/mol. (a) Write a code which asks the user to insert n, T, a, b and then plots P versus V on one figure - two plots for both equations if the volume range is (0.5arrow_forwardI need the answer as soon as possible Q4/ The ideal gas equation of states is given by: PV = nRT Where: P is the pressure, V is the volume, T is the temperature, R=0.08206 (L atm)/(mol K) is the ideal gas constant, and n is the number of moles. Real gases, especially at high pressures, deviate from this behavior. Their responses can be modeled with the van der Waals equation: nRT using matlab P- V-nb n² a v² 0 Where a and b are gas constants. For Cl₂ a = 6.579 L'atm/mol², and b = 0.0562 L/mol. (a) Write a code which asks the user to insert n, T, a, b and then plots P versus V on one figure - two plots for both equations if the volume range is (0.5arrow_forwardThe voltage V(1) (in V) and the current i(t) (in Amp) t seconds after closing the switch in the circuit shown are given by: R Vdt) = V(1– e/) i(t) = e, where t, = RC is the time constant. Consider the case where V = 24 V, R = 3800 2 and C = 4000 x 10-6 F. Determine the voltage and the current during the first 20 s after the switch is closed. Create a vector with values of times from 0 to 20 s with spacing of 2 s, and use it for calculating V(1) and i(t). Display the results in a three-column table where the values of time. voltage and current are displayed in the first, second, and third columns, respectively. (To display values in a Table, just create matrix and have its output displayed) Script ® C Reset I MATLAB Documentation 1 %Don't change the variable name 2 table =arrow_forwardLet X= (-3,-2,-1,0, 1}. Let f: X→ N by f(x) = [7z+11: The range of the function isarrow_forwardEuler's method is a numerical method for generating a table of values (xi, yi) that approximatethe solution of the differential equation y' = f(x,y) with boundary condition y(xo) = yo. The firstentry in the table is the starting point (xo , yo.). Given the entry (xi , yi ), then entry (xi+1 , yi+1) isobtained using the formula xi+1 = xi + x and yi+1 = yi + xf(xi , yi ). Where h is the small valuecalled step size. use c++ code and Use Euler's method to estimate the value of y when x = 2.5 for the solution of the differentialequation y' = x + 3y/x with the boundary condition y(1) = 1. Take x = 0.1, the exact solution ofthis differential equation is y = 2x^3- x^2.. Compare your approximation values with the exact value.arrow_forward6. Let f(n) and g(n) be non-negative functions. Show that: max(f(n), g(n)) = 0(f(n) + g(n)).arrow_forwardConsider nonnegative integer solutions of the equation x1+x2+x3+x4+x5+x6=30. How many different solutions are there? How many solutions also satisfy: for every i∈{1,2,3,4,5,6}, xi is positive and even?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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