-Kipped parTutorial ExerciseA population of a particular yeast cell develops with a constant relative growth rate of 0.4985 per hour. The initial population consists of 3.2 million cells. Find the population size (in millionsof cells) after 3 hours.Step 1dP= 0.4985Pdt0.4985PSince the relative growth rate is 0.4985 per hour, then the differential equation that models this growth with P in millions of cell and t in hours isStep 2We know that P(t) = P(0)ekt, where P(0) is the population on day zero and k is the growth rate, Substitute the values of P(0) and k into P(t) (in millions of cells).P(t) = P(0)ekt million cells7.1856million cellsSubmit Skip (you cannot come back)Need Help?Read It

Answered: Tutorial Exercise A population of a…

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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My home uses two light bulbs. On average, a light bulb lasts for 100 days (exponentially distributed). When a light bulb burns out, it takes an average of 10 days (exponentially distributed) before I replace the bulb. • Formulate a three-state birth-death model of this situation. • Determine the fraction of the time that both light bulbs are working. • Determine the fraction of the time that no light bulbs are working.
Show that for a population that satisfies the logistic model, the maximum rate of growth of population size is rK/4, attained when population size is K/2.
A scientist is studying three different cultures of bacteria {labeled "A", "B" and "C"} and wants to mathematically model the bacterial change of each type. To do this, the scientist decides to collect data for 25 consecutive days and builds the following scatter diagrams where the horizontal axis corresponds to "t" and the vertical axis to the amount of bacteria present in the culture P = P (t) Help the scientist decide which mathematical model (initial value problem) to use for each of the three types of crops. To do this, associate each of the graphs above with one of the following initial value problems. Crop type A a) dP/dt = k with P(0)=P0 and k>0.b) dP/dt = k with P(0)=P0 and k<0.c) dP/dt = kt with P(0)=P0 and k>0.d) dP/dt = kt with P(0)=P0 and k<0.e) dP/dt = kP with P(0)=P0 and k>0.f) dP/dt = kP with P(0)=P0 and k<0.g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0.h) dP/dt = kP(1-P/M) with P(0)=P0 and M, k<0. Crop type B a) dP/dt = k with P(0)=P0 and…
A material has an initial of 15 units. Which equation models the amount of the material y, decaying exponentially at a rate of 23% over time x
= 1 W = 2 % Continue = 3 Integrating Evide....docx = 4 Type here to search = 5 X Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1500 bacteria selected from this population reached the size of 1693 bacteria in three hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model. Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth. E S WRITING-CENTER_....pdf = 6 O = 7 PDF = 8 revised-summarizi....pdf T = 9 = 10 W C 11 12 Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use → 83°F Mostly clear ^ 13 Privacy Center | D Submit A 1 8.
Radioactive isotope Palyium-2021 decays at a rate proportional to the amount present. If the half-life is 1.6 thousand years, what is the decay rate per 1000 years? Give both exact answer and a percentage answer (e.g. 12.34%).
an animal species you are studying is decreasing in population. in 2020, you counted 80 animals in the habitat. in 2021, you only counted 77 animals in the habitat. what is the decay rate of this population?
A endangered species is released into a park. The population of an endangered species is expected to follow the logistic model p(t)= 810/1+8e-188t . Where t is measured in mionths. a. How many endangered species were released into the park? b. How many endangered species will there be in 5 months? c. As time goes by, what appears to be the maximum population in the park?
Bacteria is being cultured in an agar plate. It was observed that the growth of bacteria is proportional to the bacterial population itself. In an experiment done between 12:00NN and 2:00PM, the population triples. At what time should the population be 100 times than it was at noontime?
please show all working so it can be easily understood
The carrying capacity of the fish environment is 500. After 30 days, there are 100 fish in this environment. Initially, there were 20 fish. How many fish are there after 15 days? this is an exponential growth/decay problem. Please use P(t)=L/(1+be-kt) to solve. Given, L=500
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