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A: Introduction :
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- A loan account accrues interest at a rate proportional to its value. Suppose thatthis interest is compounded continuously in time at interest rate r, and supposethat payments of p dollars per year are made in a way that can be consideredto be continuous in time. write the differential equation and solveAn individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce at an initial rate of 3 parakeets per month. Write a differential equation for the population P assuming logistic growth, where the woodland can support at most 500 parakeets. (Do not round any coefficients.) dP/dt =Find the differential equation of the family of curve Straight lines with slope half the value of the x intercept
- Determine the differential equation of the family of lines with the difference of its y-intercept and x-intercept equal to 3. Show the solution.Find the differential equation (Family of Curves): Lines with slope equal to the negative reciprocal of y-intercepts.The total number of reported cases of an illness in a large city days after the start of an outbreak is modeled by the function y = F(t) that is a solution to the logistic differential equation dy/dt= (1/5600)y(1400-y). If there are 5 reported cases of the illness initially, what is the limiting value for the total number of reported cases of the illness as t increases?
- Find the differential equation of all family of straight lines at a fixed distance p from the origin.What is the differential equation of family of parabolas with vertex on the x – axis and axis parallel to the y – axisIn a certain tropical forest, “litter” [dead vegetation like leaves and vines] forms on the ground at the rate of 10 grams per square centimeter per year. At the same time, however, the litter is decomposing at the rate of 80% per year. Let f(t) be the amount of litter [in grams per square centimeter] present at time t. Find a differential equation satisfied by f(t). Then, show that this mathematical model predicts that the amount of litter in the forest will eventually stabilize. What is this ‘equilibrium level’ of litter? (Show all steps)