1. What is the equation of y = log(x) with the given transformations? Vertical compression by left by 2 unit, up by 4 units

Q: Suppose in a certain region there are 4,000 bee hives that are threatened by African bees. Initially…

A: Given, N=K1+be-rt Where  the constant K represents carrying  capacity and b is, b=KN0-1 Then, the…

Q: 12. The following graph is the 2.5 acceleration versus time for the 2 motion of a bike. If the bike…

A: We will find the total distance travelled as following.

Q: 1) Use DESMOS to graph Y = log(x – 3), show critical points. %3D

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Q: . The terminal value of an investment for T years at an annually compounded rate, r is given by VT =…

A:

Q: Consider the linear-log model given by: E(y) = 1.2 + 0.18ln(x) where y is measured in litres and x…

A: Introduction: The regression coefficient depends on the change of scale of the dependent, as well as…

Q: Find y’ when y^2 e^2x = 3y + x^2 and y(0) = 3 a. -5 b. -7 c. -6 d. -4 e. -2 f. -1 2. Find the…

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Q: Shown to the right is a certain population, in billions, for seven selected years from 1950 through…

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Q: Suppose that the growth of a certain population of bacteria satisfies dy/dt=ky where y is the…

A:

Q: Question 2 [3] A radioactive substance is decaying at a rate represented by y- h(t) - Roa', in…

A: Given: y = h(t) = R0at where 0<a<1

Q: Shown to the right is a certain population, in billions, for seven selected years from 1950 through…

A: Solution of given question is written in below steps.

Q: What is the equation of with the given transformations? Vertical compression by left by 2 unit, up…

A: shifting of curves

Q: The population in California p(t) (in million) can be approximated by the logistic growth function…

A:

Q: Suppose the function f has an initial value of 1,000 and a decay rate of 5%. Let the function g have…

A: Solution: we know that The equation of an exponential decay function is given by where a = initial…

Q: The gross domestic product (GDP) of a certain country is projected to  be N(t) = t2 + 2t + 50 ( 0 ≤…

A:

Q: Let a kind of bacteria grow in such a way that at time t sec.there are t(3/2)bacteria. Find the…

A: Given that at time t there are t3/2 bacteria.  We need to find the rate of growth at time t = 4…

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 commercial property generates income at the rate R(t). Suppose that R(0) = $70,000/year and that…

A: The formula to calculate the compound interest is given by: Compound Interest = Amount – Principal…

Q: 5. A bacteria colony grow at a rate of 11% per year. If the initial sample has a mass of 500 gram…

A: Initial mass of the bacteria P0=500 grams  growth rate r=11% per year =0.11 per year  Let size of…

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: Place the following equations into their correct category. A C f(x) 1 x 4 F(x) = 3(x+3) В D (*+3)…

A: We will use standard method to differentiate decay or growth equations.

Q: How is the graph of y =log(x) transform to produce the graph of y=log(2x)+3

A: Given graph of y = log(x), transform it to get the graph for y = log(2x) + 3.Let us first discuss…

Q: 1. Find the function of the form y = log,(x) whose graph is given. y = y 1.5 (5, 1) 1.0 0.5 5 6 -0,5…

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Q: Suppose that the population of a certain collection of rare Brazilian ants is given byP(t) = (t +…

A: To find the rate of change of population P'(t), we need to differentiate the function…

Q: Given a logistic growth function y 1 + ae the limiting value of y is - bt'

A: Given logistic growth function is

Q: 17. Suppose the radius r, height h, and volume V of a cylinder are functions of time t, and further…

A: Simply write the volume of the cylinder and differentiate with respect to h.

Q: Suppose k and / grow at constant rates given, respectively, by g, and g,. What is the growth rate of…

A: suppose k and l grow at constant rates given , respectively by gk and gl claim- to find the growth…

Q: The following graph shows the yearly industrial output (measured in billions of zonars) of the…

A: We will find the answers to all the parts as following.

Q: Suppose you want to start saving for retirement. You decide to continuously invest $15000 of your…

A: p

Q: It is estimated that x months from now, the population of a certain town will be changing at a rate…

A:

Q: 3. Determine the x-value(s) for which the function g(x) = In|x² +3x| has an instantaneous rate of…

A: Given function is Differentiating both sides with respect to x, we get

Q: 2. 18|ャ 2. 1. 1. 1. 1. y= 2 log2 x 1/4

A:

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: 1. When the interest on an investment is compounded continuously, the investment grows at a rate…

A: The change in amount with the rate r is dPdt=rP The amount of investment is 20,000. The amount of…

Q: ne of the special characteristics of any exponential growth function y= Ab' is its doubling time-the…

A: In this question, the concept of the power function is applied. Power Function Exponents are used in…

Q: 1 What is the instantaneous rate of change of Y at x = 2? O -1 none of these -1 1 3 4

A: Given : y = 1/x

Q: dy 18. x = y (log y-log x+1) (AMIETE, Summer 2004) dx Ans. log2= Cx 19. xy logdx+| y -x² log dy = 0…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. 4 20. The graph of a piecewise-linear function f. for -1<xS4. is shown above. What is the value…

A:

Q: Suppose that dP/dt - 0.18P(t) represents a mathematical model for the growth of a certain cell…

A: Given that dP/dt = 0.18 P(t)  Where P(t) is the size of culture at time t.

Q: 1. The population of a town grows at a rate proportional to the population present at time t. The…

A: We will find out the required values.

Q: Let a kind of bacteria grow in such a way that at time t sec. there are t 3/2) bacteria. Find the…

A:

Q: 4. The demand for Good x is Đ(p) = 1000 – p+ logM, where p is the price of Good x and M is the…

A:

Q: Find the linearization of the function k(x) = ln(x) when x= 1 and use it to estimate ln(1.1).

A:

Q: if f=5 is an equilibrium solution of an equation of change involving df/dx, what is the value of…

A: f=5 is an equilibrium solution of an equation of change involving dfdx.

Q: What is the equation of with the given transformations? Vertical compression by , left by 2 unit, up…

A:

Q: Suppose that the growth of a certain population of bacteria satisfies dy = ky dt where y is the…

A:

Q: 8. Without a calculator, match the functions y = 2, y = e, y = 3, y = In x, y = log x with the…

A: Without using a calculator, to match the functions, y=2x, y=e-x, y=3x, y=ln x, y=log x with the…

Q: 7. It is given that the function y=log, x has undergone the following transformations: 1. A…

A:

Q: Suppose the flow rate (in cubic feet per second, cfs) of a river in the first 11 hours after the…

A: We have given the flow rate of a river as a function