b. Find out the percentage of the limiting population of 75 frogs has been attained after 5years and after 10 years (LT – C2)c. Summarize your findings in (b) – (LT – C4) An observation indicates that the frog population Q(t) in a small pond is 25 initially andsatisfies the logistic equationQ(t)' = 0.0225Q(t) – 0.0003Q(t)²,%3D(with t in months.)

We have to solve given differential equation to find population after t years and then find…

Answered: An observation indicates that the frog…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1/2 (log.(e))" (b) dt. 2t
Suppose the probability π(x)π(x) of reaching a target (such as getting a ball between goal posts) as a function of distance x (in metres) from the target is well-fitted by a logistic regression equation withlog(π(x)/[1−π(x)])=6.1−0.13xPlease answer below to 3 significant digits.Part a)For this prediction model, what is the probability of reaching the target from a distance of 49 metres.Part b)At what distance is the probability of reaching the target equal to 0.6?
The following table shows world population N, in billions, in the given year. According to the logistic model N = 10.90 / 1+2.23e^-0.030t, when will world population reach 90% of carrying capacity? Year N 1965 3.38 1970 3.72 1975 4.15 1980 4.48 1985 4.87 1990 5.38 1995 5.72 1999 6.05 a) 2064b) 2069c) 2066d) 2094
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5. Differentiate the following natural log and e functions. a. b. C. y' = y' = y' 11 y" = y = In(12 - x - 5x²1) y = In(e-x + xe-x) y = x² In (8x)
Suppose the population of a species of animals on an island is governed by the logistic model with relative rate of growth k = 0.05 and carrying capacity M= 15000. I.e., the population function P(t) satisfies the equation P' = bP(15000 - P), where b = k/M. If the current population is P(0) = 20000, which one of the following is closest to P(1)? O a) 19700 O b) 19890 Oc) 19680 Od) 19690 Oe) 19805 Of) 19742 Motion
At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) 20 y = dy dt = 1 +9e 8 g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.) 9.79 hr (d) Write a logistic differential equation that models the growth rate of the culture's weight. Then repeat part (b) using Euler's Method with a step size of h = 1. (Round your answer to the nearest whole number.) y(5) = 6 -0.3662t = 1.37 0.366y| 1 (1-20) (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) X g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
A study of Maryland's portion of Chesapeake Bay found the following information about stocks of market-sized oysters.† In 1994, the stocks were 218 million. (This is the number you will use for the initial population N(0).) The carrying capacity is 5089 million oysters. The intrinsic exponential growth rate is 0.274 per year. (a) Find a logistic model N(t) for the number, in millions, of market-sized oysters. Take t to be the time in years since 1994. (Rround all regression parameters to three decimal places.) N(t) = (b) Plot the graph of the model you found in part (a) over the first 20 years. (c) How many market-sized oysters does your model predict for 2007? Round your answer, in millions, to the nearest whole number. million oysters (d) The actual number of market-sized oysters was found to be 82 million. Use the Internet to find possible explanations for the reduced levels of oysters in Chesapeake Bay.
It is expected in traditional mathematics that when you input data into a well-defined equation you get an expected output. We looked at the logistic equation f(x) = rx(1-x) with different initial inputs. Explain how with some initial conditions we get a predictable result but with others the result was surprisingly different - how was it different?
The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?
Suppose A = 500(1.045)t . Compute dA/dt
Suppose that a company expects its annual profits t years from now to be f(t) dollars and that interest is considered to be compounded continuously at an annual rater. Then the present value of all future profits can be shown to be Find FP if r = 0.08 and f(t) = 100, 000 + 1000t. The present value is dollars. = f et f(t) dt FP =

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An observation indicates that the frog population Q(t) in a small pond is 25 initially and satisfies the logistic equation Q(t)' = 0.0225Q(t) – 0.0003Q(t)², %3D