A population of a particular yeast cell develops with a constant relative growth rate of 0.4651 per hour. The initial population consists of 3.4 million cells. Find the population size (in millions of cells) after 6 hours.

A population of a particular yeast cell develops with a constant relative growth rate of 0.4651 per hour. The initial population consists of 3.4 million cells. Find the population size (in millions of cells) after 6 hours.

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...

See similar textbooks

Related questions

Q: The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1%…

Q: Personal care aid is an occupation that is growing quickly. Assume that, in a certain region there…

A: Given information:The number of personal care aids in 2024 is 157,500, which is a growth of 28% over…

Q: A sample of bacteria experienced 5% daily growth compounded continuously for 14 days. At the end of…

Q: Suppose the population of a town is 8,600 and is growing 3% each year. Predict the population after…

A: Population in 1 year = 8600 + 8600*3/100 =8858 Population…

Q: The production of a gold mine decreases by 5% per year. What is the approximate half-life for the…

Q: Use a growth rate of 1.4% to predict the population in 2061 of a country that in the year 2006 had…

A: Given, the population in 2006 = 100 million Growth rate(r)=1.4%=0.014

Q: Personal care aide is an occupation that is growing quickly. Assume that, in a certain region,…

Q: Uranium 235 is used as fuel for some nuclear reactors. It has a half-life of 710 million years. How…

Q: A hospital prepares a 200 mg supply of molybdenum-99 which has a half-life of 66 hours. How much…

Q: The bacteria in a laboratory culture increased from an initial population of 500 to 2000 in four…

A: We can express this growth using the formula for exponential growthN(t)=N0⋅ertN(t) is the population…

Q: Personal care aide is an occupation that is growing quickly. Assume that, in a certain region,…

Q: 100 mg of a medication is administered to a patient. After 7 hours, only 22 mg remains in the…

Q: Assume that a population of E. coli bacteria doubles every 20 minutes. Construct a table that shows…

A: Given that, The population of E. coli bacteria doubles every 20 minutes. Initially Population start…

Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

Q: If an initial population Po of bacteria doubles in 6 hours, how long will it take to triple (grow to…

A: Given that 6 hours to take doubles the initial population

Q: Personal care aide is an occupation that is growing quickly. Assume that, in a certain region,…

Q: Acertain virus swept through a town of 1000 people. The virus caused illness that lasted an average…

A: Consider the SIR model, dStdt=-ast·ItdItdt=ast·It-bItdRmtdt=bIt where a,b are real parameters of…

Q: Nobelium is a radioactive isotope that has 25 seconds half-life. How long will it take for Nobelium…

A: The formula to calculate the amount of radioactive isotope is N=Noe-λt where N is the rest amount No…

Q: Suppose 16 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

Q: A bacteria has an initial population of 500 and is doubling every hour. The bacteria reaches a…

Q: Personal care aide is an occupation that is growing quickly. Assume that, in a certain region,…

A: The number of personal care aids in 2024 is 195,686, which is a growth of 29% over 2014.Denote y as…

Q: Personal care aide is an occupation that is growing quickly. Assume that, in a certain region, tehre…

A: Consider that in 2014 the number of personal care aides is x.

Q: in a certain region, there will be a need for 150,146 personal care aides in 2024, a growth of…

A: It is an important part of statistics. It is widely used.

Q: Suppose that a population in a particular city is 46,581 in 2010. What is the population after 15…

A: The population growth is modelled using the equation: N(t)=N01+rt, where N0 is the initial…

Q: A bacteria culture doubles every – h. At time 1-h an estimate of 40 000 is taken. 4 4 What was the…

Q: Personal care aide is an occupation that is growing quickly. Assume that, in a certain region,…

A: Personal care aide is an occupation that is growing quickly. Assume that, in a certain region,…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

100%

A population of a particular yeast cell develops with a constant relative growth rate of 0.4651 per hour. The
initial population consists of 3.4 million cells. Find the population size (in millions of cells) after 6 hours.

Since the relative growth rate is 0.4651 per hour, then the differential equation that models this growth with P
dP
in millions of cell and t in hours is
dt

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

The population of an endangered species decreases at a rate of 7% per year. Approximately how long will it take the population to decrease to half of its current size?
A bacteria culture had a population of 13 million at 10:00 am and by 2:00 pm had grown to 21 million. Predict the population at 6:00 pm that same day.
Personal care aide is an occupation that is growing quickly. Assume that, in a certain region, there will be a need for 175,179 personal care aides in 2024, a growth of about 25% over 2014 levels. How many personal care aides were there in this region in 2014?
At the beginning of the last decade, a total of 7.2 million passengers took a cruise vacation. The global cruising industry has been growing at approximately 7% per year. Assume that this growth rate continues. Suppose N = (t) gives the number of passengers, in millions, that take a cruise vacation at year t. Answer parts (a), (b), (c), and (d) of the question. Click VERIFY to move to the next part. (a) Report the following. Use the pull-down menu to indicate the units. A0) = Number Click for List (b) If (t) is written in the form a-b’, do you predict the value of b to be greater than 1 or less than 1? O b is greater than 1 O b is less than 1 (c) Complete the boxes below to write a formula which gives N as a function of t, where t is in years. Do not round any values. Since your formula gives N in millions of people, check that it passes through the initial value x = 0, N= 7.2, as opposed to passing through x = 0, y = 7,200,000. N= Number ( Number (d) How many millions of cruise…
What is the continuous growth rate of the colony? Round to the nearesthundredth of a percent.
Personal care aide is an occupation that is growing quickly. Assume that, in a certain region, there will be a need for 120,334 personal care aides in 2024, a growth of about 20% over 2014 levels. How many personal care aides were there in this region in 2014
An assortment of 100 fish is put into a fish tank; the fish population grows at a continuous rate of 23% per hour. How long until the population doubles in size? (round to the nearest fish)