complete and conscientious work Write out‚ number‚ and letter all questions Use regular font for the questions Use bold font for your answers 1) Explain how the logistic population growth model modifies the exponential population growth model to incorporate the idea of resource limitation? Exponential growth is possible only when infinite natural resources are available; this is not the case in the real world. Individuals will compete (with members of their own or other species) for limited resources
Premium Population ecology Population Population growth
Trigonometry and Statistics) A. Functions 1. Demonstrate knowledge and skill related to functions in general 1.1 Define a function 1.2 Differentiate a function from a mere relation * real life relationships * set of ordered pairs * graph of a given set of ordered pairs * vertical line test * given equation 1.3 Illustrate the meaning of the functional notation f(x) 1.4 Determine the value of f(x) given a value for x B. Linear Functions 1. Demonstrate knowledge and
Premium Function
.........3 RECOMMENDED 2-UNIT OPTIONS......................................................4 MATHEMATICAL MODELLING............................................................4 UNIT 1: ALGEBRA‚ GEOMETRY AND CALCULUS MODULE 1 : BASIC ALGEBRA AND FUNCTIONS...........................7 MODULE 2 : TRIGONOMETRY AND PLANE GEOMETRY .............18 MODULE 3 : CALCULUS I ..............................................................23 UNIT 2: ANALYSIS‚ MATRICES AND COMPLEX NUMBERS MODULE 1 : CALCULUS II .
Premium Mathematics Function Quadratic equation
of a and b 2) A function f is defined as f(x) = for x 1 = - for x = 1. Show that f(x) is differentiable at x = 1 and find its value 3) Let f(x) = if x 2 = k‚ if x = 2. If f(x) is continuous for all x‚ then find the value of k. 4) Let f(x) be a function of x defined as f(x) = ‚ x 1 = ‚ x = 1. Discuss the continuity of function at x = 1 5) Determine
Premium Derivative Function Calculus
n calculus‚ Rolle’s theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. ------------------------------------------------- Standard version of the theorem [edit] If a real-valued function f is continuous on a closed interval [a‚ b]‚ differentiable on the open interval (a‚ b)‚ and f(a) = f(b)‚ then there
Premium Calculus Derivative Function
looking for at Store A. In Store A‚ the bracelet without charms costs $85 and each charm costs $15. A. Use function notation that models the total price of the bracelet and how that price is based on the number of charms. Explain the reasoning behind your equation. 15W=85 IN ORDER TO FIND THE NUMBER OF CHARMS YOU NEED YOU HAVE TO DIVIDE. B. What would be a reasonable domain for this function based on this scenario? Explain why this is a proper domain. C. If Marco and his sisters have saved $250
Premium Derivative Function Object-oriented programming
__ The total amount of revenue made by the Miramar Resort Hotel is given by the function ‚ ‚ where x is the amount of money the hotel spends on advertising its services‚ and where both revenue and x are measured in thousands. 1. Using Wolfram Alpha‚ graph the revenue function over the given domain and paste the graph here. 2. Compute the marginal revenue function and copy and paste a graph of this function on the domain here. Then use Wolfram Alpha to determine where revenue is increasing
Premium Function Derivative
coordinates of all relative extreme points of[pic]. |A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] | [pic] First find the derivative of the function[pic]‚ f ’(x): |[pic] |= |[pic] |apply power rule of differentiation | | |= |[pic] |simplify
Premium Function Calculus Derivative
Name: Date: Graded Assignment Checkup: Graphing Polynomial Functions Answer the following questions using what you’ve learned from this unit. Write your responses in the space provided‚ and turn the assignment in to your instructor. For problems 1 – 5‚ state the x- and y-intercepts for each function. 1. x-intercept: (0‚ 0)‚ (-4‚ 0)‚ (0‚ 0) y-intercept: (0‚ 0) 2. x-intercept: (1‚ 0) (0‚ 0) (-4‚ 0) y-intercept: (0‚ 4) 3. x-intercept: (-1‚ 0) (0‚ 0) (0‚ 0) y-intercept: (0‚ 0) 4
Premium Maxima and minima Polynomial Calculus
1. 7.5/8 The height in metres of a ball dropped from the top of the CN Tower is given by h(t)= -4.9t2+450‚ where t is time elapsed in seconds. (a) Draw the graph of h with respect to time (b) Find the average velocity for the first 2 seconds after the ball was dropped h(0)=(0‚450)‚ h(2)=(2‚430.4) = (430.4-450)/(2-0) = -9.8m/s √ (c) Find the average velocity for the following time intervals (1) 1 ≤ t ≤ 4 h(1)=(1‚445.1) h(4)=(4‚371.6) = (371.6-445.1)/(4-1) = -24.5m/s √ (2) 1 ≤ t ≤ 2 h(1)=(1‚445
Premium Derivative Velocity Function