A population P obeys the logistic model. It satisfies the equation dp 2 dt = 500...
2. Suppose a population P(t) satisfies the logistic differential equation dP dt = 0.1P 1 − P 2000 P(0) = 100 Find the following: a) P(20) b) When will the population reach 1200? 2. Suppose a population P(t) satisfies the logistic differential equation 2P = 0.1P (1–2000) = 0.1P | P(0) = 100 2000 Find the following: a) P(20) b) When will the population reach 1200?
3 pts) Suppose that a population develops according to the logistic equation dP dt = 0.15P - 0.0006P2 where t is measured in weeks. a) What is the carriying capacity? b) Is the solution increasing or decreasing when P is between() and the carriying capacity? C) Is the solution increasing or decreasing when P is greater than the carriying capacity? Note: You can earn partial credit on this problem.
Suppose that a population of hacteria grows according to the logistic differential equation dP =0.01P-0.0002P2 dt where Pis the population measured in thousands and t is time measured in days. Logistic growth differential equations are often quite difficult to solve. Instead, you will analyze its direction field to acquire infom ation about the solutions to this differential equation. a) Calculate the maximum population M that the sumounding environment can austain. (Note this is also calked the "canying capacity"). Hint: Rewrite...
(1 point) Any population, P, for which we can ignore immigration, satisfies dP Birth rate – Death rate. dt For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population. Thus, the population of such a type of organism satisfies a differential equation of the form dP аP? — ЬР with a, b > 0. dt This problem investigates the solutions to...
If a quantity y satisfies the differential equation dy = kx(10-y), k>0 dx. when X = 2 and y = -7, the graph of yir increasing decreasing constant cannot be determined
dP [20pt] 7. Suppose that the certain population obeys the logistics equation = 0.025 - P. (1 - dt where C is the carrying capacity. If the initial population Po= C/3, find the time t* at which the initial population has doubled, i.e., find time tº such that P(t) = 2P = 2C/3.
Differential equations question. dp/dt = 0.3 (1-p/10) (p/10-2)p 1. (5 points) Consider the given population model, where P(t) is the population at time t A. For what values of P is the population in equilibrium? B. For what values of P is it increasing? C. For what values is it decreasing? : (i-T-YE -2) p dt120 her
f 5. (See 2.5, 16) Two models used in population modeling are the Logistic equation and Gompertz equation: dy dt dy = (r-ay)y and where r,a>0 are constant dt a) For both, sketch the graph of f(y) versus y, find the critical points, and determine asymptotic stability. (b) For 0 y a, determine where the graph of y versus t is concave up and where it is concave down. (c) Sketch solution curves near critical points, discussing differences in the...
show works please Q71 5 Points A population is modeled by dP Р = 9P1 dt 2500 (a) For what values of P is the population increasing? (b) For what values of P is the population decreasing? (c) What are the equilibrium solutions? Upload your file showing your work. Please select file(s) Select file(s) Q7.2 5 Points Solve the differential equation and show your work. dz + 7e2z+t = 0 dt
1. Show that the following languae is context-free: {amb” cm:n, m >0} U {CPb9qP : P, q>0}