Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 9800. The number of fish tripled in the first year. a) assuming that the size of the fish population satisfies the logistic equation (image attached) determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k =  P(t) = b) How long will it take for the population to increase to 4900 (half of the carrying capacity)?  It will take .                           years

Q: V1+ x² dx 2.

A: Follow the procedure given below

Q: Solve the equation. |4 - 2x| - 5 = 5 Select the correct choice below and, if necessary, fill in the ...

A: Given :- |4 - 2x| - 5 = 5 |4 - 2x| = 10 For The Negative Case : - (4 - 2x) = 10 2x - 4 = 10 2x = 14 ...

Q: coS X =dx sin? x

A:

Q: Find the slope and y-intercept of the given line, and graph it. Av 6y = - 7x The slope of the line i...

A: Answer: The solution is as follows:

Q: Find the derivative of the function. y = 9Vx y' = %3D

A: Our Aim is to find the derivative of y=9x -(i)

Q: Use synthetic division to divide (2x*- 3x³ - 5) + (x +2). State the quotient and the remainder.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first quest...

Q: 1. S(x² – 2)² dx

A: Solving the problem by doing the integration.

Q: Find the infinite sum (if it exists): 00 i=0 If the sum does not exists, type DNE in the answer blan...

A: We need to find the infinite sum.Below find the detailed solution in the image.

Q: A wheel turns 1,800 revolutions per minute. How fast does it turn in radians per second? Type pi for...

A:

Q: A rumor spreads through a school. Let y(t) be the fraction of the population that has heard the rumo...

A:

Q: RAGLIO Use a table of values to estimate the value of the limit of lim Vx + 4 – 2 2. f(x) f(x)

A:

Q: Choose the correct graph of y = sin x, - T < x < 2 T; and y = csc x, - T < X< 2T: 2 1 27 -1 -2

A:

Q: The given function is not one-to-one. 9(x) = (x- 3)2 y 10 -10 -5 10 -5 -10 Restrict its domain so th...

A:

Q: Construct a difference table to predict the next term of the sequence. –50, –68, –78, –80, –74, –60,...

A: Arithmetic series 

Q: 1. Complete the table below. Ordinary or Partial Linear or Non- Order Independent Dependent Variable...

A:

Q: Determine if the given function is continuous and differentiable at the indicated values of x. Write...

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple questio...

Q: 2. Given f(x) = 3x – 2 and g(x) =+, find each of the following: (a) (f o g) (z) (b) (go f) (x)

A:

Q: 6. Evaluate the following integral: [sin 8x cos 5x dx

A:

Q: 3 Select the function that is even. f(x) = 3sin(x) f(x) = 3tan(x) f(x) = 3cot(x) f(x) = 3cos(x)

A:

Q: -3 dz Find S 225922=4

A:

Q: Use Maple to solve the problem. (1) Utilize Maple to find the derivative. Include a graph containing...

A:

Q: Solve for the derivative of y IMPLICITLY 22 + Væ3 + 2y= y²

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Differentiate the following functions. No need to simplify. a. f(x) 1 V6x + 5° + In(a*) = 7x7

A: We have to find derivative of f(x)

Q: Lesson 7 CL Activity # 1 #4 4. S(x) = (2x-6)* 4. f(x) =- (x+3) (2х-6)

A: We are asked to find the second deritives.

Q: A ball is dropped from a height of 15 feet and bounces. Suppose that each bounce is 5/8 of the heigh...

A:

Q: The trough below is full of water. Recall that water has weight density 62.4 lb/ft³. 2 ft 5 ft 8 ft ...

A:

Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: The graph above is a transformation of the function f(x) Write an equation for the function graphed ...

A: The given graph is:

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find...

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: COSX (25) Find the area between the curve y= and x-axis and x 1/2, x 1/6 sin x

A:

Q: secx 5. When does the graph of the function f(x) have a horizontal tangent? 1+ tanx

A:

Q: 10. Solve for the derivative of y IMPLICITLY 22 + Vx³ + 2y = y² %3D

A:

Q: An average of 40,000 people visit Riverside Park each day in the summer. The park charges $15.00 for...

A: given that, number of people =40000 ticket price=$15 and for each $1 increase in price,the park woul...

Q: The profit made when t units are sold, t>0, is given by P =t - 26t + 168. Determine the number of un...

A:

Q: 8. Find f-1 of the one-to-one function f (x) =and state the domain and the range of f and f-1. x-3

A:

Q: Determine whether the function x2 + 2 x > 2 f(x) = x = 2 is continuous at the 4х — 2 x < 2 given poi...

A: First of all we will find the left hand limit at X equal to 2 and then find the right hand limit X e...

Q: Determine whether the function x2 + 2 x > 2 f(x) = { 6 = 2 is continuous at the 4x x < 2 - given poi...

A:

Q: Solve the initial value problem. d?y = 3 - e 2", y(1) = - 2, y'(1) = 4 dt?

A: Given that: d2ydt2=3-e2t, y(1)=-2, y'(1)=4

Q: 4. -6 -3 -3 -2 -1/ The graph above is a transformation of the function x² Write an equation for the ...

A:

Q: Determine the a) vertex, b) focus, c) directrix, d) axis of symmetry, and e) opening of the parabola...

A:

Q: Salve for x if Arc tan (1- x) + Arc tan (1 + x) = Arc tan

A: Our Aim is to solve for 'x' if tan-11-x+tan-11+x=tan-1x -(i)

Q: Identify the quadric surface each of the following equations represent and sketch its graph. O 92" +...

A: 9 x2 + 4y2 + 36 z2 = 369 x236+4 y236+36 z236=1x24+y29+z21=1x222+y232+z212=1

Q: Provide a diagram where limx→a f(x) exists, f(a) is not defined and f(x) is not continuous at a. Wha...

A: A function f(x) has properties,limx→af(x) exits, f(a) is not definedfx is not continuous at x=a cont...

Q: Show the diagram/graph showing the points at with each arch passes through: ? Dimensions of the tun...

A: Given:    y=-18361x2+18

Q: 4. The graph of the function f(x)= /16-x² is a half-circle. If we shift this graph 2 units to the le...

A:

Q: Choose the correct graph of y = cos x, -T< x< T: 37 2

A: Given the query is find the graph of the cos function.

Q: 1. If x'y-xy'+x' +y = 0 find y. %3D

A:

Q: 10. Solve for the derivative of y IMPLICITLY 22 + Væ³ + 2y= y²

A: Note: According to our expert guidelines only first individual question is to be answered, kindly re...

Q: 2 dse the Reimann Integral to evaluate S v'dv.

A:

Q: 1. To raise a complex number to a power in polar form, you raise the power and multiply the by the p...

A: Given that: Complex Numbers