. Logs with different bases Show that f(x) = logax and g(x) log, x, where a > 1 and b > 1, grow at a comparable rate as %3D

Q: Let exp(x) denotes the exponential function e. If f(1) = exp(zi),z >0. %3D then the minimum value of…

A: Consider the given function fx=ex1x

Q: Exponentials with different bases Show that ƒ(x) = ax growsfaster than g(x) = bx as x→ ∞ if 1 < b…

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Q: Another equation that has been used to model population growth is the Gompertz15 equation dydt=ry…

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Q: The Weber-Fechner law states that if Y is the physical intensity of sound and X is the perceived…

A: From the given information, fY(y)=ye-y22, y>0 And X=klog(Y)Xk=logYeXk=Yexk*1k=dydx

Q: # 1) If V is the volume of a cube with edge length x and the cube expands as time passes, find dV/dt…

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Q: For the discrete logistic equation Xt + 1 = cxt(1 - xt) and the given values of xo and c, calculate…

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Q: A 15-gram sample of radioactive iodine decays in such a an that the mass remaining after t days is…

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Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: Find the linear approximation of f(x) = lnx at x = 1 and use it to estimate ln(1.02). L(x) =…

A: Given that: f(x)=lnx

Q: 3) Show that for any constants M, k, and a, the function (",) A(1 - ) y(t) 1 ·M|1+tanh ´k(t – a)…

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Q: The volume of a cylinder is given by V = πr²h, where r is the radius of the cylinder and h is the…

A: From the give information, The volume of a cylinder is given by V = πr²h μr = 1.6 and σ²r = 0.04 ,…

Q: Consider one-parameter members of exponential family of the form, 8(yl0)= exp{d(@)+S(y)+c(0)T(y)},…

A: Given See the handwritten solution

Q: Dala fram 4 Study of Tho airlines wich ly to Sucell Town. If one flight is selected Find P(on time…

A: Note : as per policy I have calculated first main qquestion kindly REPOST for remaining  here given…

Q: Suppose that a certain population obeys the logistic equation dy = Ty dt K a) If yo K find the time…

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Q: The logistic equation for the population p (in thousands) at time t of a certain species is given by…

A: 1st find equilibrium  solution and then find sign of dpdt to draw direction field and then conclude…

Q: log x y = dy dx 5+5ln5logx x² In5 dy 5-5ln5log x dx x² In5 Option 4 Op tion 3 dy _ 5-5ln5logx x² In5…

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Q: A function is approximated by a cubic spline defined by: 25/12 30.0833 An approximation of ff(x)dx…

A: Sol:- Consider the function in the range of (0,1) ∫011+x+x2+x3dxApply the Sum Rule:…

Q: Find the slope of the tangent line to the graph of x²-Iny=0 at x=2 O None of these O 4e4 O e4 O 4

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Q: A bacterial culture is growing according to the logistic growth function           y = 1.25 /(1 +…

A: a) The weight of the culture after 0 hours is calculated as follows:…

Q: In a study, a cancerous tumor was found to have a volume of f (t) = 1.8253(1 - 1.6e-0.4196t)3…

A: Consider the given function of the volume of cancerous tumor after t weeks, ft=1.82531-1.6…

Q: 10.2.2 Use a cobweb to show that x* =0 is globally stable for 0<r< Tin the 1 logistic map.

A: As per the question we have to construct the cobweb diagram for the logistics map : xn+1 = rxn(1-xn)…

Q: The integrating factor of the given DE are already given below. What is the value of "n"…

A: A differential equation is an equation that relates the variable and it's derivatives. Solution of…

Q: A culture of bacteria doubles every minute. What is the model P(t) for this growth? a. P(t) Pgeina…

A: We will find out the required model

Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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Q: In each of the following, find pdf of Y a) Y= X2 and  fX(x) = 1, 0 0 c) Y = eX  and fX(x) = 1/σ2 *…

A: Given: Then:

Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: az dz +y =5 ax If z= log ( x+x*y+y° ), Prove that x

A: We can prove this using the rules of partial derivative

Q: Suppose that dP/dt = 0.13P(t) represents a mathematical model for the growth of a certain cell…

A: Answer and explanation is given below...

Q: If X is an exponential r.v. with parameter 5, identify the r.v. 10X

A: Introduction: The random variable X has an exponential probability distribution with parameter, λ =…

Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

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Q: 1. Let X be a lifetime (in hours) of a lightbulb and suppose that X has a PDF of (e0.001x f(x) = {…

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Q: Can you help me step by step?

A: dA/dt may be written as,

Q: Show that -E{t, log(sigma(w*x)) + (1 – t;) log(1 – sigma(w"x;))} = E, log(1+ e-yw* x %3D Where…

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Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA in…

A: Area of a Circle = πr2As the circle expands as time passes

Q: A small manufacturing business has a group life insurance contract on it employees. Suppose that the…

A: Given, Lognormal distribution: E(S) = 0.085 V(S) = 25.32

Q: In the Romer model output is given by ü = e where j = ALy = A(1-sR) %3D Assume that = ALA Further…

A: Introduction:-

Q: Determine for the following function: dy dx y = log3 (x² + 1) ○ (z²+1) In 3 2x O (1²+1) 2x O 2x…

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Q: a) the linear approxinma ion to the function + 3X ät

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Q: b) Assume the rate of investment is given by the function K' (t) = 1(t) = In t Compute the total…

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Q: Determine the expression of the integrating function if it is known that: e) S; f(x)dx : - sen(9) +…

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Q: A logistic initial value problem is given by dP — kP(М — Р), P(0) — Ро. dt M Po i. Show that P(t) Ро…

A: Part (i):   First separate the logistic equation and integrate it by using the partial fraction:…

Q: Show that the following functions all grow at the same rate using properties as x co: fi(x) = x°,…

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Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) : -M1+ tanh = 2 2 у satisfies…

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Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: 7 = f x² logx dx 3

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Q: For the scatterplot on the right, determine which, if any, of these functions might be used as a…

A: Let's find.

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the…

A: To Show- Show that for any constants M, k, and a, the function yt = 12M1 + tanhkt - a2 satisfies the…

Q: (a) Show that z = 0 is the unique branch point of f(z) = log(z)

A: Since you have posted a multiple question ,I will solve the first question (i.e(a))  for you. To get…

Q: (2) Differentiate the following w.r.t.x (i) cos (x + a²) (ii) ve+2) + 5 (iii) n log tan (iv) Vtan Vx

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…