In Discrete Math, for growth functions ( Bio O, Omega, Theta): When it  comes to proof, what exactly is the k value when we need c and k. C is obvious when f(x) <= c(g(x)) . Also, is the abs always required or not necessary.

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: Find the first six terms of the expansion of the function e^x log(1+ y)

A: We have to find the first six terms of the expansion of the function              exlog1 + y Here ,…

Q: It is estimated that a worker in a shop that makes picture frames can paint y frames t hours after…

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Q: Find the order of growth for the following function.  = (3n^5+4n^4+5n^2+4)/(8n^2+7n+2)

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Q: Find the exponential function f(x)=a^x that passes through the point (−3,1/27) and has a y-intercept…

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Q: f (t) is of exponential order at infinity.

A: By fundamental theorem of calculus, we have f(t)=f(0)-∫0tf'(u) duAlso, since f' is piecewise…

Q: A certain species of alligators is to be introduced into a swamp, and wildlife experts estimate the…

A: Given that

Q: The annual net sales (revenue) earned by Nintendo in the fiscal years 2000-2014, can be approximated…

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Q: Find the exponential function of the form h(x)=ba^x + c such that  y=2 is a horizontal asymptote…

A: Topic:- calculus

Q: Find the equation of the vertical asymptote f(x)=log(x+5)

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Q: a. For what values of b>0 does b* grow faster than e* as x→00? ах b. Compare the growth rates of ex…

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Q: Experimentally, the number of bacteria in cultivation duplicates for each hour. If there are 1000…

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Q: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

A: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

Q: certain species of alligators is to be introduced into a swamp, and wildlife experts estimate the…

A: A certain species of alligators is to be introduced into a swamp, and wildlife experts estimate the…

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: If f(x) and g(x) is any function then, If limx→∞f(x)g(x)=∞ then f(x) grows faster than g(x). If…

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: Suppose that P dollars in principal is invested for t years at the given interest rates with…

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Q: Employ the concept of growth of functions to compute the smallest intege for which the function f(x)…

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Q: Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.17 percent…

A: Given,  Continuous rate of population is 0.17 percent a year. Population in 1988 was 6.6 million  To…

Q: A bank account earns 12% interest, compounded continuously, and has an initial balance of zero.…

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Q: (For Bacteriologists). In one of your Basic Calculus sessions, a top of the class Grade- 12 student…

A: Hair we have to find out the value of Y for the different values of T

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: Find the equation of the vertical asymptote f(x) = log(x + 5)

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Q: Order the functions f(x) = log2 x, g(x) = xx , h(x) = x2 , and k(x) = 2x from the one with the…

A: Consider the given functions fx=1og2x,gx=xx,gx=x2,k=2x.

Q: Find the equation of the vertical asymptote f(x) = log(x + 4)

A: Given,                f(x)= log(x+4)

Q: Find the equation of the vertical asymptote f(x)= log(x+1)

A: The equation of the vertical asymptote f(x)= log(x+1)

Q: find the formula for an exponential funtion that passes through the two points given  (x,y)=…

A: Given  (x,y)= (0,6600) and (x,y)= (2,66)

Q: The function f(t)=(et)10 is of exponential order?   True  False ?

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Q: Suppose that dP/dt = 0.19P(t) represents a mathematical model for the growth of a certain cell…

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Q: Fit an exponential curve of the form y = ab* to the followin 1 3 4 6. 1.0 1.2 1.8 2.5 3.6 4.7

A: Introduction: The graphical method has the disadvantage that the straight line drawn may not be…

Q: Q2 Let X,X, f(r;8) = e/",I > 0. (i) Show that f(x:0) is a member of the exponential class. (ii) Find…

A: X1, X2, ...., Xn is a random sample from f(x,θ). We first calculate the likelihood function. If it…

Q: 2. An art collector purchased for $1000 a painting by an artist whose works are currently increasing…

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Q: Prove that the straight line y = 3 - 2x intersects the exponential curve y =e^x x at a point whose…

A: y=3-2x  and  y=exat f(x)=3-2x-ex

Q: ompany is considering an investment that requires an immediate investment of $475,000 and an…

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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: . Find the exponential functions of the form f(x) = ab* that pass through 1) (-2, 32) and (1, –)

A: An exponential function is in the general form f(x) = abx We know the points (-2,32) and (1,1/2) ,…

Q: B. A certain culture is able to sustain 100 colonies of bacteria. Initially, there were 10 colonies…

A: We need to find colonies after 24 hours.

Q: Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept…

A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

Q: Find the exponential function f(x)=a whose graph is given as:

A: From the graph we can see that the value of function at x = -1 is f(-1) = 3   Now we will look the…

Q: Find the exponential function f(x)=ab^x that satisfies the conditions f(0)=−3 and f(3)=−24

A: The exponential function f(x)=ab^x that satisfies the conditions f(0)=−3 and f(3)=−24

Q: The number of bacteria in a certain sample increases according to the following function, where y,…

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Q: The number of bacteria in a certain sample increases according to the following function, where y,…

A: The number of bacteria in a certain sample increasesy=y0e0.0264 t

Q: Use the Gompertz growth model, y = Le y = Sketch its graph. L = 9000; y = 900 when t = 0; y = 1125…

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Q: In Exercises, sketch the shifted exponential curves y = -1 - ex and y = -1 - e-x

A: We will use transformation to sketch from the parent function f(x)=e^x This means f(x) will reflect…

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

A: Here, the given function is: y(t)=12M1+tanhk(t-a)2...(1)

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: Find the order of growth for the following function.  = (7n^5) + (2n^3) (log(n))

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Q: Suppose f E C" (IR). Show directly that a fixed point xo is exponentially stable if f' (xo) 0.

A: When f'x0&lt;0, the function is decreasing at x0 and when f'x0&gt;0, the function is increasing x0.…

Q: The number of Drosophila fruit flies in a controlled experiment assumes the following growth pattern…

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