1. Exponential growth and decay can be expressed as A(t) = Apekt, where A(t) = the amount at time t A(0), the initial amount (the amount at t = 0) relative rate of growth or decay Ao k t = time The model describes exponential growth if k is The model describes exponential decay if k is

Q: Differentiate the following. (a) y = sin(x4) (b) y = sin(x) Solution (a) If y = sin(x4), then the…

A:

Q: Let a = (9,5) and 6 = (5, -3). Compute the following vector projections. proja b projz a =

A:

Q: 16. The length of a rectangle is increasing at a rate of 6 cm/min and the width is decreasing at a…

A:

Q: - Find the area of a parallelogram formed by the vectors PQ and PR, where P = ( − 4, – 4, — 6), Q =…

A: See the details solution in below

Q: 5-8 The graph of a function f is shown. Does f satisfy the hypotheses of the Mean Value Theorem on…

A:

Q: A 140 ft length of steel chain weighing 20 lb/ft is dangling from a pulley. How much work is…

A: Recall: Work done=Force (F)* Displacement(t)

Q: Estimate using the linearization L(x) of f(x) (Use decimal notation. Give your answer to five…

A:

Q: 41. Sales saturation. The Gottahavit device is introduced in a market with 150,000,000 potential…

A: It is given that the unit sales are modelled by the following function:…

Q: A store owner want to develop a new snack mix by mixing chocolate and trail mix. How many pounds of…

A: Cost of chocolate per pound =$ 13.8 Cost of trail mix per pound =$ 4.4

Q: Find the differential of the function. y = e³x dy = =

A: We have given function  y=e3x dydx=ddxe3x dydx=e3x·ddx3x dydx=e3x·3 dydx=3e3x dy=3e3x dx

Q: Estimate using the linearization L(x) of f(x)=√√ at a = at a = 49. (Use decimal notation. Give your…

A: Given that , fx=1x Estimate 152 using the linearization Lx of fx at a=49.

Q: You Must solve the whole question completely. Don't solve partially one or two questions. If u don't…

A: Given, y=3x-6

Q: Given the function below ✓50x³ + 75 Find the equation of the tangent line to the graph of the…

A: Given, f(x)=50x3+753

Q: 5-6 The graph of the derivative f' of a function f is shown (a) On what intervals is f increasing?…

A: Topic- Application of derivatives We are given graph of f'(x) and we know that f(x) is increasing…

Q: Find all points on the curve 5xy² - 10x²y = 5 where it has a horizontal tangent line. Write each…

A:

Q: 5. Find the arc length of each curve (integrate by hand) b) y = x/2 on [0,60] a) x = -8y-3 on [-2,6]…

A: Given data, a) x=-8y-3 on -2,6 b) y=13x32

Q: A company buys a machine for $475,000 that depreciates at a rate of 30% per year. Find a formula for…

A:

Q: Directions: Consider the following function f(x). Use the logarithmic laws to rewrite this function…

A:

Q: Which one of the following shaded-regions in the plane consists of all points whose polar…

A:

Q: What is the angle in radians between the vectors a= <-1₁8, 4) and b (2₁-5,107 Angle: Tradians. F

A:

Q: Find the domain of the vector-valued functions: R(t) = √t² - 9 î+ In]t − 3] ƒ + (t² + 2t − 8) k B.…

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

Q: Compute the area of the region enclosed by the y-axis and the curve in the xy-plane given by the…

A: Given parametric equations x(t) = t2 − 6t  and  y(t)=10t3 + 9t

Q: Evaluate the definite integral. (This one is challenging) [ ² da z²ln(x + 1) dx = ( ½ ln (2) — -— -…

A:

Q: Evaluate the following integrals using substitution(s) 1. √ 2x(x² + 1) ²³ dx 2. [4e³x dx 3. [(1 +…

A: To evaluate : ∫2xx2+123dx ; ∫4e5x ; ∫1+cosx2dx We have to evaluate the above mentioned integrals…

Q: Please see the attached image and answer the

A:

Q: Find a vector orthogonal to both (2,3,0) and to (0,3,4) of the form. 41,0, 07 for olmas

A:

Q: Solve the equation. Give a general formula for all the solutions. List six solutions. 1 2 cos (20) =…

A:

Q: y + 1 (x-4)² Graph the boundary of the domain of z below. Let z(x, y) =

A: Domain of the given function is as follows with red lines.  The line  x = 4 is not in our domain…

Q: If y = O 2-3' then -12 (2-3)² 12 dy dx

A: To find derivative of given function.

Q: (5) Solve the initial value problem: Ay" - 4y + y = 0; 3₁(x) = e¹/²; y(0) = 2, y'(0) = 2.

A:

Q: Let y = 5x² + 5x + 2. If Ax estimate Ay Δy ~ = 0.2 at x = 5, use linear approximation to

A: Given that,

Q: Consider following ODES: 1)4y" +12y' +13y=0,2) 2y″ +7y' + 5y = 0 a) Find characteristic equation and…

A:

Q: A light truck with manual transmission has a circular brake drum with a diameter of d 300…

A: Solved Below

Q: Compute the area of the region enclosed by the line  y=x−5 and the parabola y2 = 2x + 70

A:

Q: 1. 2. y"" +3y" +4y +12y = 8cos2x - 16sin2x y" - y'= -2(1+x) +4e* -6e-* +96e³x

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: 37-38 Explain, in terms of linear approximations or differen- tials, why the approximation is…

A: We are required to prove that 4.02  ≈2.005 using the method of linear approximations

Q: An isotope of the element erbium has a half-life of approximately 9 hours. Initially there are 13…

A:

Q: m If a rock is thrown upward on an exoplanet of a nearby star with initial velocity of 25- S meters…

A: NOTE: Refresh your page if you can't see any equations. . the position function of the rock after t…

Q: Given f(x)= = - 3x + 15 x + 2 and g(x)= = - 2x + 6 x-4 - The domain is all real numbers except x =…

A:

Q: The position of a free-falling object is given by s(t) = -4.9t² + vot + so where s(t) is measured in…

A: Note : As per our Guidelines , we can solve first three subparts .Please repost remaining subparts .

Q: Find r(t) .u(t). r(t) = (7t − 7)i + ½t³j + 3k u(t) = ²i - 6j + 1³k r(t)u(t)= Is the result a…

A:

Q: 5. f3-* dx 6. S √ √√9-t² 7. S- 1-e²t dt dt

A:

Q: 34. f(x) = x² + 250 X (0, 0)

A: 34) f(x) = x2 + 250xfor find extrema   f'(x) = 0 &amp;for minima f''(x) &gt;0 for minima f''(x)…

Q: If it is exact find a function F(x, y) whose differential, dF(x, y) gives the differential equation.…

A:

Q: Prove that |Re(2−7+z²)| ≤ 4 when |z|≤1.

A:

Q: Please graph the ellipse (x+3)^2/4 + (y-4)^2/16 = 1 Please name the coordinates of the center,…

A: The given equation of the ellipse:x+324+y-4216=1which can be written as:x+3222+y-4242=1

Q: Directions: Consider the following function f(x). Use the logarithmic laws to rewrite this function…

A:

Q: 3. The population of Sometown was 12,000 in 2000 and grew to 15,000 in 2010. Assume that the popu-…

A:

Q: d) f(x) = x sin x + cos x [0, 2π]

A:

Q: 2) A company produces and sells smartphones. The revenue for one smartphone is $900. The cost to…

A: NOTE: Refresh your page if you can't see any equations. . the give cost function is  where x is the…