State True or False in each of the following cases. In one or two sentences justifiy each of your answers providing examples if relevant.   Every one-dimensional first order ODE population model is a gradient system

raph the following discrete-time dynamical systems, find the equilibria algebraically, and check whether the stability derived from the Slope Criterion for stability matches that found with cobwebbing. f (x) = x² for 0 ≤ x ≤ 2

City Hall wishes to learn about the rate of parking mater use. They choose 8 Downton blocks at random and on each block they choose 5 meters at random. Six weeks are chosen randomly from the year, and the usage on each meter is measured everyday for all the meters in those weeks.Write out an appropriate linear model

Linear Algebra Now use the Massey Method with a 10 max point differential for the following system:During the Early Part of the Season: Team B beats C by 8 points. Team D beats E by 5 points.During the Middle Part of the Season: Team A beats D by 10 points. Team E beats C by 5 points.During the Later Part of the Season: Team A beats E by 4. Team E beats B by 20 points. a. Draw a directed graph of this season. b. Write the system of equations for this season using the Massey method. c. Solve the system (using least squares) to find the ratings for each team, and use those ratings to rank them

State True or False in each of the following cases. In one or two sentences justifiy each of your answers providing examples if relevant. A (linear or nonlinear) population model can have a spiralling stable equilibrium point at the origin.

. Two neighborhoods, A and B, are identical: Each has 100 housing units; all housing units are of the same size and quality. 100 blue households and 100 red households will be living in these two neighborhoods. The two racial groups’ rent premium curves are as follows:   Identify the three equilibria.  For each equilibrium, determine whether it is stable or not. Please explain your answer.

(6) Population Modeling with Discrete Dynamical Linear Systems. We now discuss populations with discrete breeding seasons, where reproduc- tion is limited to a particluar season of the year. For example, let's consider the number of female ruby-throated hummingbirds in a population with an annual breeding season of March to July. A female usually lays one clutch of two eggs; sometimes two clutches are laid. We will assume that the average life span of a female hummingbird is four years. We define the age of a bird at the END of a breeding season as follows: age zero (0) : any bird that is born during the current breeding season age one (1): any zero-year old bird which survives to the end of the next breeding season age two (2): any one-year old bird which survives to the end of the next breeding season age three (3): any two-year old bird which survives to the end of the next breeding season We make the following assumptions about the reproductive viability of female birds: age zero…

Please answer asap. Do not answer if you already did and do not use answers from other sources.

Suppose that a patient receives a daily dose of 50mg/L of a certain drug such that 42% of it is eliminated from the body each day. If on a certain Monday, the concentration of the drug measured in their body (shortly after the daily dose) is 55 mg/L, write down the Discrete-Time Dynamical System describing the dynamics of the concentration xt of the drug in the body (in mg/L, t days after that Monday). Then write down the general solution to this DTDS.

A manufacturing company has three processing lines. Each processing line combines various raw materials to produce the same output, Y. One of the processing lines can combine units of input (X) to produce units of output (Y) such that there is a linear relationship between X and Y. The Chief Executive Officer wants the output model to be estimated for this processing line. Given the values of X and Y (in thousands of units) in the table below, and as the Director of Data Management, you are to: x 5 7 2 8 4   8 12 6 14 8 Determine the extent to which output changes as the input change and interpret your result. Find the intercept of the output model and interpret it. Write down the equation of the line of best fit for output. Determine the value of the extent of relationship between input (X) and output (Y), and interpret your result.