The predator satiation model for population growth specifies that the reproductive rate of an organism as a function of the total population varies according to the formula,rpR(p) =1 + kpwhere p is the total population in thousands of organisms, r and k are constants that depend on the particular circumstances and the organism being studied, and R(p) is the reproduction rate in new organisms per hour. tGiven that k = 0.4 and r = 0.09, find R'(p).R'(p) =Find R'(5), (Round your answer to four decimal places.)R'(5) =x thousand organisms per hour, per one thousand organismsInterpret the result.This means that the reproduction rate of organisms in a culture containingorganisms is increasing v v at a rate ofX organisms per hour, per one thousand additional organisms.

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Answered: The predator satiation model for…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Initially, 10 grams of a radioactive substance were found in a sample. It was observed that 20% of the initial amount of radioactive substance disintegrated after 2 hours (that is, 8 grams remain after 2 hours). Find the half-life of the radioactive substance (that is, the time it takes for one- half of the initial amount to disintegrate) if the rate of disintegration of the radioactive substance is In z 1 2 0.7 proportional to the amount of the substance present at time t. You must begin your solution process by 3 considering the proportional relationship presented below. Use the natural logarithm table to the right 1.1 to provide an approximate answer. Your work must support your answer. 4 1.4 1.6 dA a A 6 1.8 dt 1.9 2.1 9 2.2 10 2.3 7,
Suppose a person's utility function for items x and y is u = ln(x) + ln(y), and he currently has $200 in his pocket, and the price of x is $10 per item and the price of y is $20 per item, find the combination that maximises his utility.
In a city with a fixed population N, the time rate of change of the number P of people who have heard a certain rumor is proportional to the produc of P and NP. Suppose initially 25% have heard the rumor and after one week this number has grown to 50%. What percentage will this number reach after one more week? After one more week, the percentage is %. Your final answer needs to be a fraction. Also, keep in mind that we are working with percent. Submit
The air in a room with volume 180 m³ contains 0.3% carbon dioxide initially. Fresher air with only 0.05% carbon dioxide flows into the room at a rate of 2 m³/min and the mixed air flows out at the same rate. Find the percentage p of carbon dioxide in the room as a function of time t (in minutes). p(t) = 0.5556e % +0.7 X What happens to the percentage of carbon dioxide in the room in the long run? lim p(t) = 0.007 X %
Newton’s law of cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e., the temperature of its surroundings). We let (t) denote time, T(t) be the temperature of the object at time (t), (T0 = T(0)) (the object’s temperature at (t = 0)), and Tomg be the constant ambient temperature. Set u(t) = T(t) - Tomg and show from Newton’s law of cooling that (u) satisfies the initial value problem (*) u’(t) = ku(t), u(0) = T0 - Tomg for a constant (k). Solve the initial value problem (*), i.e., find u(t)) (expressed in terms of (k), T0, and Tomg . Find T(t).
A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there are100 milligrams of the material present and if after two years it is observed that 5 percent of the original mass has decayed, find (a) an expression for the mass at any time t and (b) the time necessary for 10 percent of the original mass to have decayed.
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Near the surface of the earth, a ball (with p = 0.1) is released from rest and its flight through the air offers resistance that is proportional to its velocity. How long will it take the ball to reach one-half of its terminal velocity? How far will it travel during this time?
A mobile phone company records their annual sales on 31 December every year. Paul thinks that the annual sales, S million, can be modelled by the equation S= ab', where a ar b are both positive constants and t is the number of years since 31st December 2015. Paul tests his theory by using the annual sales figures from 31t December 2015 to 31st Decemb 2019. He plots these results on a graph, with t on the horizontal axis and log,,S on the vertic axis. (a) Explain why, if Paul's model is correct, the results should lie on a straight line of best fit on h graph. The results lie on a straight line of best fit which has a gradient of 0.146 and an intercept on vertical axis of 0.583. (b) Use these values to obtain estimates for a and b, correct to 2 significant figures. (c) Use this model to predict the year in which, on the 31st December, the annual sales wvould fi be recorded as greater than 200 million. (d) Give a reason why this prediction may not be reliable.

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