To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t) of rats alive at time t (inmonths) satisfies the Gompertz differential equationdydtwith M = 204 and k = 0.13.Rat populationP(t)20010010203040Time (months)Find P(t). Note that P(0) = 200.(Express numbers in exact form. Use symbolic notation and fractions where needed.)P(t) =Determine the population after 15 months.(Round your answer to the nearest integer.)population after 15 months:rat(s)

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Answered: To model mortality in a population of…

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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During the period from 1790 to 1920, a country's population P(t) (t in years) grew from 3.6 million to 101.6 million. Throughout this period, P(t) remained close to the solution of the initial value problem -0.0001494P² P(0) = 3.6. dP dt = 0.03136P-( (a) What 1920 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 259 million. Has this logistic equation continued since 1920 to accurately model the country's population? (a) The logistic equation predicts the population in 1920 to be million. (Do not round until the final answer. Then round to the nearest thousandth as needed.) K AI C H TU U →> C ¢ ➡ H i O + 2.4 e В → نه Y + - 8 .... : *** 5 Ø Co Less . N 0 .. H A E X U i 9 A C ש Σ VI 8 FR > in X

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To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t) of rats alive at time t (in months) satisfies the Gompertz differential equation