64-69. Steady states If a function f represents a system that varies in time, theexistence of lim f(t) means that the system reaches a steady state (or equilibrium).For the following systems, determine whether a steady state exists and give thesteady-state value.250064. The population of a bacteria culture is given by p(t)t+13500t65. The population of a culture of tumor cells is given by p(t)t+1

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Answered: 64–69. Steady states If a function f…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter1: Expressions And Functions

Section1.8: Interpreting Graphs Of Functions

Problem 19PPS

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1. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous? 2. If the demand of firm is QD (p) = 50 -3p and its supply function is Qs (p) = 14 + 6p. What is the equilibrium? 3. Find Lim x2 -4x + 3/5
Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=
evaluate (a) lim x→ x^2 - 36/x^2 + 5x - 6 (b) the demand curve of a firm is p= -10q + 5900 and its average cost is A(q) = 2q^2 - 4q + 140 + 845/q. where q is the firm's output produced and sold. 1. derive an expression for the total revenue of the firm. 2. derive an expression for the firm's total profit function 3. derive an expression for the rate of change of profit function of the firm. 4. is the rate of change of profit increasing or decreasing when the firm's output level is q= 50? 5. determine the level of output for which the total profit of the firm is maximized 6. what is the firm's maximum profit
12. Consider that the inflation rate in a six-year period in Mexico behaves according to the function i(T)=t^2 - t + 3Calculate the minimum value of inflation and the time in which it reaches this value. Consider the domain of the function [0,6] and the time in years. Provide the graphic behavior of inflation during the six-year period.In what interval does I(+) decrease? That is, there is deflation.
(a) Find the following: i. Lim →x/ + 9x/ 6x/ − 4x/ii. Lim →(2x − 1)/ − 3 x − 5(b) The total revenue curve of a firm is R(q) = 40q − 12q and its average cost A(q) =1 30q − 12.85q + 20 +400 q,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?
Concave up (or positive concavity) over an interval means that... Group of answer choices a.as the independent quantity increases, the function over successive equally-sized intervals decreases. b.as the independent quantity increases, the function's average rates of change over successive equally-sized intervals are positive. c.as the independent quantity increases, the function over successive equally-sized intervals increases. d.as the independent quantity increases, the function's average rates of change over successive equally-sized intervals increase. e. as the independent quantity increases, the function's average rates of change over successive equally-sized intervals decrease.
1. A critical number of f′(x) is an inflection point of f(x).True or False 2. If the radius of a circle is increasing at a constant rate, then so is the circumference.True or False 3. If two variables x and y are functions of t and are related by the equationy = 1 −x^2, then dy/dt = −2x.True or False 4. When finding the global minimum of a function on an interval, you must usethe first or second derivative test to verify that your point is a global minimum.True or False
If a diver of mass m stands at the end of a diving board with length L and linear density ρ, then the board takes on the shape of the graph of y = f(x),where EIy ″ = mg(L − x) +1/2 ρg(L − x)2. E and I are positive constants that depend on the material of the board, and g (< 0) is the acceleration due to gravity. The x y coordinate plane is given. A diving board modeled by a function graph starts at the origin nearly horizontal, goes down and right becoming more steep, and stops in the fourth quadrant. A diver stands with feet at the right end of the board. (a) Find an expression for the shape of the curve. f(x) = y = Use f(L) to estimate the distance below the horizontal at the end of the board. −f(L) =
1.Identify the kind of function. 2.Find the x- and y- intercepts and the vertical abs horizontal asymptotes. 3.Find the end behavior of the function (y,y)
13. Find the minimum and maximum value of the function on the giveninterval.y = 2x 2 + 4x + 5 [-2, 2]
a. Write the equation of a function with a vertical asymptote at x = −2 , a removable discontinuity atx = 1, and a horizontal asymptote at y = 0. b. Write the equation of a function with a vertical asymptote at x = 1, a removable discontinuity atx = −2 , and a horizontal asymptote at y = 5
Find the absolute maximum and absolute minimum of the function f ( x ) = x 2 e -x on the closed interval [ 1 , 4 ].

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