Math

CalculusQ&A LibraryThe population of a town with a 2016 population of 63,000 grows at a rate of 2.3% per year. a. Find the rate constant k and use it to devise an exponential growth function that fits the given data. b. In what year will the population reach 105,000? a. Find the rate constant k. an exact answer.) (TypeStart your trial now! First week only $4.99!*arrow_forward*

Question

a) and b) please

1 Rating

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: a. Determine whether the Mean Value Theorem applies to the function f(x)= ex on the given interval [...

A: Definition used: Mean Value Theorem

Q: Find the area of the region that lies inside both curves. r = 9 + cos(θ), r = 9 − cos(θ)

A: To calculate the area of the given region (by integration) described by polar coordinates

Q: Find the area, in square units, bounded above by f(x)=6x2 −2x−19 and below by g(x)=7x2 +12x+21.

A: f(x)=6x2 −2x−19 and g(x) = 7x2 +12x+21.As a first step, we need to find the point of intersection of...

Q: A and B please!

A: Given,

Q: The revenue from the sale of a product is, in dollars, R = 1500x + 3000(3x + 3)−1 − 1000 where x i...

A: The revenue from the sale of a product is, in dollars,R = 1500x + 3000(3x + 3)−1 − 1000where x is th...

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=<x2 , -y2, z2>...

A: The vector field is given as

Q: 3. Given the function g(x) 8x defined on [-1, 1], determine if the function satisfies the Mean Value...

A: Given,

Q: The total profit (in dollars) from the production and sale of x calendars if P(x)= 22x-0.02x2-500; 0...

A: It is given that, the total profit from the production and sale of x calendar is P(x)=22x–0.02x2–500...

Q: Find the work required to move the object on the line segment. Please refer to attached image.

A: As a first step we need to parameterize the curve C. The curve has two points (1, 4, 1) and (4, 16, ...

Q: Find the area of the following surface using a parametric description of the surface. The cap of t...

A: Consider the surface that is the cap of sphere:

Q: What is the solution to the initial value problem below? y′=5ex +8x3 +x2 +4x y(0)=3 Do not include "...

A: The given differential equation is, y′=5ex +8x3 +x2 +4x.

Q: SImplify (h3-4h)/(h3-2h2)

A: Simplify the given expression as follows.

Q: 1) The substitution u = tanx gives∫(sec2x.tanx)dx = ∫(x)du = 1/2.u2 + C = 1/2.tan2x + CThe substitut...

A: Yes, both integrations are correct by their respective substitutions.Reason:An integral of a functio...

Q: p(q)=2q2-4q+5; q=2 (a) Find the derivative, by using the definition. (b) Find the instantaneous rate...

A: Part (a)The derivative of p(q) at any point q, by using the definition, will be given by the express...

Q: What's the domain of x-1 / (1 - e^(x - 3))

A: Since this function is a rational function, the denominator can't be equal to 0.

Q: For the sequence 1, 4, 7, 10,..., its nth term is Preview My Answers Submit Answers ou have attempte...

A: The given sequence is 1,4,7,10, ...

Q: find the critical numbers of the function g(theta) = 4(theta)-tan(theta). My question is from the sc...

A: Refer to the question as per screenshot provided, I have to answer the how the last step came.That i...

Q: find the derivative of the question in the picture please show all work

A: Obtain the derivative of the function.

Q: Use the derivative f'(x) = (x - 3)(x + 4)(x + 4) to determine the maxima and minima of f and the int...

A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because a...

Q: Usel'Hôpital'sRule to find the following limit.

A: To use L'Hopital's rule we try to get 0/0 form or infinity/infinity form first. We write x^2*cotx as...

Q: Help me please..

A: The Taylor series for cosx at x=0.

Q: Calculate the derivative of the function y = (6^6 + 3)^x using the fact that b^x = e^(x ln b) and by...

A: Consider the given function:

Q: A mass hanging from a spring is set in motion and its ensuing velocity is given by v(t) = -2 sin (pi...

A: To find the position function we integrate velocity function and use s(0)=2.Answer(A): Position func...

Q: graph quadratic function f(x) = -3x2- 12x -1

A: Consider the given equation

Q: How can I do this? Which is the result?

A: Given:The function is

Q: 150 100 50 20 40 60 3. Suppose that a population develops according to the logistic equation (c) Use...

A: Given that a population develops according to the logistic equation

Q: The DeWitt Company has found that the rate of change of its average cost for product is C'(x)=(1/4)-...

A: Given information:The DeWitt Company has found that the rate of change of its average cost for produ...

Q: b. Find the area of the region bounded by Y = xe ax and the x-axis on the interval 0,41, where a> 0....

A: Area of region which is bounded by f(x) and x-axis on [0,4] computed as follows.

Q: suppose the line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the line tang...

A: Given information:The line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the...

Q: How do you find the limit of f(x) of the attached equation?

A: Notice that the graph is discontinuous at x=3.

Q: Find the relative maxima, relative minima, horizontal points of inflection, and sketch the graph for...

A: The given function is,

Q: Determine whether the following statements are true and give an explanation or counterexample.

A: Given information:

Q: 1000 Find the marginal cost when q = 10. 9 The average coste for producing q units of a product is g...

A: The average cost c is given by ,

Q: y = t(lnt)2 Find the derivative

A: According to the chain rule of derivative,Using the above rule, where u = t and v = ln t

Q: FIND THE DERIVATIVE OF THE FUNCTIONy=0.6e to the fifth(x) degree

A: The given function "y" is shown on the white board. We need to find its derivative. Before we get in...

Q: (3x2+5)8x-92 fy(1x4 + x2 logarithmic differentiation gives y (32+5)(8r-92 1x44+x2 16 2x 3x2+5 6-x9 6...

A: We have to find derivative using lograthmic differentiation .Question is given below:

Q: How can I get the result? Which is the result?

A: Use online graphing calculator to graph of the function.

Q: The function f in the figure satisfies the lim f(x)=3 as x -> 2. Determine the largest value of ...

A: (A) We find the range of f(x) using |f(x)-3|<1.

Q: Use the derivative f' to determine local minima and maxima of f and the intervals of increase and de...

A: When f'(x)>0 then f(x) is increasing. Answer: f(x) is increasing in (-4pi/3,-pi)U(-2pi/3,-pi/3)U(...

Q: Please help

A: Here we will make the use of series for sin(x2) to solve the given integral.The provided integral is...

Q: a), b) and c) please. I also forgot how to write interval notation....

A: To find the direction we have to graph the function v(t)= 3t^2-36t+105 ; [0,8]. And then we check th...

Q: Is y=e6x −3x−2 a solution to the differential equation shown below? y′−6y=7x+3

A: Here given differential equation is:Find the solution of given differential equation and match the g...

Q: 2. Given the given function f(x) = x+defined on the interval [1, 3], determine if the function satis...

A: The given function is continuous and differentiable on the whole real numbers except zero. In partic...

Q: The beginning of the question is attached. How do I argue that f(x) is concave if and only if g(x)=...

A: A function is concave or ceonvex is defined by the sign of its double derivative.A function is conve...

Q: What is Calculus

A: Refer to the question what is calculus,It is topic of maths which helps in studying curves, and find...

Q: The consumer price index (CPI) measures how prices have changed for consumers. With 1995 as a refere...

A: Given:The rate of change of CPI in dollars per year is dC/dt= 0.009t2 − 0.096t + 4.85, where t repre...

Q: A train is initially traveling at a rate of 5 miles per hour. The acceleration of the train is 5 mil...

A: Given: The acceleration of the train is 5 miles per hour squared. That is, a(t) = 5.The initial velo...

Q: If y 3 , then dx 5x2-3 10r2 3V/5x2-34 35x2- 3) 5x2-3 10x 3 3(5x2-3)2 10r 3 35x2-3)

A: Find the derivative of the given function.

Q: a. find a possible function f and number a b. evaluate the limit by computing f`(a).

A: We first write the given function in the form of the definition of the derivative.

Q: Suppose that the cost funtion for a commodity is C(x)= 300+6x+1/20x^2 dollars (a) Find the marginal...

A: The given Cost function for a commodity is C(x) = 300 + 6x + (1/20)x2.(a) To find the marginal cost ...