Consider a one-dimensional growth c(x, t) of phytoplankton in a water mass. Formulate the model describing the dynamics of growth taking into account the following: D , its diffusion coefficient, r its rate of growth, R its mortality rate due to sinking. Fixing the area of interest as 0 ≤ x ≤ 2 and the initial concentration of phytoplankton as 30moles/ 3 cm , find the concentration distribution of phytoplankton in 0 ≤ x ≤ 2 at any time t .
The growth dynamics of phytoplankton in a one-dimensional water column can be modeled using the diffusion-reaction equation: \[ \frac{\partial c}{\partial t} = D \frac{\partial^2 c}{\partial x^2} + r c - R c \] where: - \( c(x, t) \) is the concentration ____ __________ _______ _____ _________ _____ _____ _____ _____ _____ _______ ____.
____ _________ _________ __________ ___ _______ _____ _________ _____ _________.
____ ________ ___ _______ ____.
__________ ____ ____ _________ ________ ___ ___ _________ __________ _________ __________.
______ _________ ________ ___ ____ ________ ____ _____ _______.
________ __________ ________ ______ _______ ______ _______ ________ ________ ________.
_________ ___ ___ ___ _______ ____ _______ ________ ___ _____.
_______ __________ ______ _____ ____ _______ __________ ________.
_________ _____ ______ ___ _____.
_______ ____ _____ ____ __________ _______ _________ ____ ____ ___ ______.
__________ _____ ____ _______ ______ _________ _____ _________ _________ _______ _________.
_____ ________ __________ _____ ______ __________ ____ ____ _____ ________ ____ ___.
___ ____ ____ _____ _______ ________ ___.
__________ __________ ___ _________ _________ _________ _____ _________ __________ ________.
___ _______ ______ ___ __________ ___ _________ ________ _____ ________ ____ _______.
_________ _______ ___ _________ _____ ____ _________ _________ ____ ___.
______ ____ ___ __________ _____ ________ _____ _____.
__________ _____ __________ _____ ________ ________ ___.
_____ ________ _____ __________ ___.
___ _____ ____ ___ ___ ________ _______ __________ _____ __________ _____.
__________ _______ ______ __________ _____ ________.
________ ______ _________ __________ ____ ____ ______ ______.
_____ _________ _____ ______ ___ ________ _________ ______ _______ ____ _________ ________.
______.
Get Full Answer on WhatsApp
Suppose that the previous forecast was 2090 and the actual value of the variable of interest for the period was 1985 and the oldest value of interest was 1955. Using the moving average technique based upon the most recent four observations find new forecast for the next period.
A string of length l is connected to a fixed point at one end and to a stick of mass m at the other. The stick is whirling in a circle at constant velocity v . Use dimensional analysis to find the equation of the force in the string.
A monopolist sets a price ‘p’ per unit and the quantity demanded ‘q’ is given by the following relation:
Let there be a fixed cost of Rs.9 and a marginal cost of Rs.1 per unit.
i) Write the profit function of monopolist.
ii) For maximum profit, find the number ‘x’ of units produced. Also find the maximum profit.
iii) A potential entrant enters into the business of the monopolist. He believes that the monopolist will go on making ‘x’ units. Write the profit function of the entrant.
iv) For maximum profit of entrant, find the number ‘z’ of units produced.
v) Find the maximum profit of the entrant. Explain whether he should enter into the business or not.
vi) Find the profit made by the monopolist after the entrant has entered into business.
Characterise the following as discrete or continuous giving reasons for your answers.
i) Effects of radiation treatment on a tumour when applied for short period of time but at regular intervals.
ii) Effects of chemotherapy drugs on a tumour when introduced into a patient for a given duration of time.
A projectile is fixed with a constant speed v at two different angles of projection α and β such that it gives the same range. Show that
State two real-world problems where you think that mathematical modelling is the only approach to find the solution of the problem. Give 4 essentials for each of the problems. Why do you think that there is no other scientific alternative for the treatment of these problems.
Consider the following system of equations
Find the nature of the critical point ,0( of the corresponding linear system.