The population of rats grows exponentially with time. A zoologist predicted that the population of the rats in the forest grows at a rate of 14.2% every 3 months. TASK 1: If there are 2,000 rats in the forest this month, construct a function that will show the population of the rats after months. Include the representation of variables. TASK 2: Show the graph of the function using Desmos. Include the graph of the asymptote/s. TASK 3: What will be the population of the rats in the forest after a year (round off to the nearest whole number)?

Q: Let A = 1 2 5 3 -1 3 3 1 4 2 a 4 Find the solutions of Ar= b for all a. B. b -1 8 B

A:

Q: Find a 3*3 symmetric matrox A so tht the characteristic polynomial of A is P(x) = x^2(3-x) and the…

A: Kindly refer to Step 2 for the solution.

Q: The table shows the total personal income in the United States (in billions of dollars) for selected…

A: Here, x represents number of years since 1960 and y represents income (in billions of dollars) after…

Q: Question 4 (4). We want to show that ex > 0 regardless if x is positive or negative. Supppone x. 30.…

A:

Q: min=m2 -n2 Is associative on Z. O True O False

A: Associative properties  Let a,b,c in Z then the associative property is  a*b*c=a*(b*c)

Q: For the vector field G = (yety + 4 cos(4x + y))i + (xey + cos(4x + y)) 5 I find the line integral of…

A:

Q: Mary invested in an account that grows 2.25% interest every month. a. If she invested Php 15,000…

A: When the interest is compounded, then the formula used is A=P1+rnnt , where, A is the final amount,…

Q: y''' — 4y'' + 13y' + 50y y(0) = 4, y'(0) = 10, y’’(0) = 42 y(t) = = 0

A:

Q: Let v1 vector=[−4  h] and v2 vector =[−10   20]   (check image for reference) Then span(v1…

A:

Q: 100 me A television producer designed a program that will include a comedy and advertisements. The…

A: The linear function that needs to be optimized is called the objective function. The objective…

Q: Which of the following statements hold for the minimal polynomial of a matrix B. (i) The minimal…

A:

Q: A parabolic stream of water is spraying out of a hole in the floor two feet behind Veronica. The…

A: Let the equation of the parabola be x-a2=-by-c  (since concave down) Let the water is flowing out of…

Q: Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx², c < 0

A: Introduction:  Quasi-Concave:           The function f is quasi-concave if and only if for every s,…

Q: Consider the linear system: AX = b, Where A E Rmxn with linearly independent columns, and b E Rm.…

A: The best solution for x is x = AT A-1 AT bThe QR transformation of A is A = QR, where Q is matrix of…

Q: Which of the following structures is a field? (Z9, +, X). An integral domain with 81 elements. O The…

A: A commutative ring R (|R|&gt;1)with unity is called a field if every nonzero elements of R is a…

Q: A = 2 4 −1 0 -2 9 , B = D= 0 −1 3 1) Use the above matrices to compute the following (where…

A:

Q: Consider the Euclidean inner product space R³ with a basis B = {(1,1,1),(0,1,1),(0,0,1)}. 3 Find an…

A:

Q: Determine the order of the differential equation + x²y = xex. dx A. 0 B. 1 C. 2 D. 3

A:

Q: Let km:R2 R2 be linear maps and M (k)= 21 N 32 linear map km (the composition of linear maps) is and…

A:

Q: The population of rats grows exponentially with time. A zoologist predicted that the population of…

A: Here we use differential approch for the second part.

Q: 5. Two species struggling to compete against each other in the same environment have populations at…

A: The given equations are: x't=3xt-4yt                    (1)y't=-2xt+yt                  (2)…

Q: 1 Which of the following is a second-order linear nonhomogenous ODE? A) sin(x)y" + y = 0 B) sin(x)y"…

A:

Q: Suppose you want to buy a $140,000 home. You found a bank that offers a 30-year loan at 5.1% APR.…

A:

Q: For every square matrix A in M (C) there is a nonzero polynomial f(x) 4 O True O False over C such…

A: In this problem  we have to tell that given statement is true or false  given statement is  For…

Q: Eliminate the parameter and describe the shape of the curve: :=√√x+4; _y=3√t; for 0≤t≤16

A:

Q: 3 (d²x)². 7 2 y (dx)² + y ² (dx) ² + 3y || 5x

A: Order of a differential equation  The order of the differential equation is highest order of the…

Q: The Euclidean inner product (2u-v, 3u +4v) 4v)=

A:

Q: If the matrix of change of basis from the basis B to the basis B' is 302 A = 20 A. B. - 01 1 column…

A:

Q: 4.33. (a) Evaluate f (x+2y) dx + (y-2x) dy around the ellipse C defined by x = 4 cos 0, y = 3 sin 0,…

A:

Q: Ex12. Let L:R5 → Rª be defined by X y ·10 L = V W 1 1 2 0 -1 3 0 0 2 0 -1 5 - 1 - 0 X y Z V W ● a)…

A:

Q: solve #4 please, Show all of your work on pictures and explain each step you make. Thank you!

A:

Q: 90° The right-angle triangle has two legs and a hypotenuse. Leg 1 is = 4.2 in. Leg 2 is 8.8 in. =…

A: For any right angled triangle: Pythagorean's formula: h=p2+b2, h is the hypotenuse, p is the…

Q: S is a solid in the first octant that is bounded by z = x2 + y2 and the following planes: z = 2, y =…

A: Given that, S is a solid in the first octant that is bounded by z=x2+y2 and the following…

Q: 1+rx ≤ (1+x) Also, show that the equality holds only if x = O. Hint: Apply the Mean Value Theorem to…

A: To Prove: 1+xr≥rx+1 for x&gt;-1, r&gt;0 using Mean value theorem. Also prove that equality occurs…

Q: have the following theorem. THEOREM 4.3.2 The zeros of sinh zand cosh z are given, respectively, nmi…

A:

Q: In the vector space P, of polynomials of degree at most two, then the first column f the matrix of…

A:

Q: K = {at² + bt + c | a ≥ 0, b, c € R} ℃ P₂. S = {p = P₂|p(1) = 0}.

A: Find the basis and determine whether there is a subspace in these 2 subsets.   K=at2+bt+c | a≥0, b,c…

Q: In the vector space P₂ of polynomials of degree at most two, then the first column f the matrix of…

A: Given that P2 is a vector space containing the polynomials of degree at most 2.  B={ e1=1+x,…

Q: 1 2 3 4 5 6 7 Which of the following is a second-order linear nonhomogenous ODE? A) sin(x)y" + y = 0…

A:

Q: Solve the following linear system by Gauss elimination. If the system is inconsisitent, type "NA" in…

A: Given system of linear equations:-2b+8c=103a+12b-9c=-99a+34b-19c=-16

Q: Consider the basis B = {(2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

Q: Q8 A

A:

Q: where B = P-¹AP. STEP 1: First note that A 3 00 0 -2 0 0 0 1 P-¹AP = = || |B| = 13 11 13([ STEP 3:…

A:

Q: Eliminate the arbitrary constant in the following equation: x³ - 3x²y = C.

A:

Q: Let A CR be measurable with m(A) > 0. Prove the following statements: a. There exists r >0 such that…

A:

Q: Let A C R be measurable with m(A) > 0. Prove that there exists r > 0 such that A - AC (-r,r), where…

A: Given Data: To prove that there exists r&gt;0 such that A-A ⊂-r,r,where A-A :=a1-a2 :a1,a2∈A

Q: The following vectors are linearly independent in R4 u1 = (0,0,-7,1) u2 = (1,-2,0,5) u3=(0,0,0,-4)…

A:

Q: Monthly Temperature The data below represent the average monthly temperatures for Baltimore,…

A: x x2 y xi-x¯2 xi-x¯yi-y xi-x¯xi2-x2 xi2-x22 xi2-x2yi-y 1 1 31.8 30.25 128.15 292.419 2826.73…

Q: Define T: P₂ → P₂ by Find the eigenvalues. (Enter your answers from smallest to largest.) (21, 22,…

A:

Q: 5. A group of 10 students in MATH 105 start a walking program. The chart below shows each member's…

A: