Assume that the number of bacteria follows an exponential growth model: P(t) = Poekt. The count in the bacteria culture was 800 after 20 minutes and 2000 after 30 minutes. (a) What was the initial size of the culture? (b) Find the population after 75 minutes. (c) How many minutes after the start of the experiment will the population reach 14000? Note: webwork usually expects four significant digits so don't round your answers.

Assume that the number of bacteria follows an exponential growth model: P(t) = Poekt. The count in the bacteria culture was 800 after 20 minutes and 2000 after 30 minutes. (a) What was the initial size of the culture? (b) Find the population after 75 minutes. (c) How many minutes after the start of the experiment will the population reach 14000? Note: webwork usually expects four significant digits so don't round your answers.

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: Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt. The count in the…

Q: A bacterian culture has a initial population of 10000. If its population declines to 5000 in 6…

A: Exponential model ⇒Pt=Ae-kt⇒A=initial population ⇒k=decay rate ⇒t=Time in hours⇒Pt=Population at…

Q: bacillus subtilis, a type of a bacteria responsible for the decomposition of organic matter, grows…

Q: Angelina takes a 375 mg aspirin for her headache. The amount of aspirin remaining in her system…

A: Given- Vivian takes a 375 mg aspirin for her headache and the amount of the aspirin decrease…

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: AIT student places 100 bacteria into a petri dish. Six hours later, he measures 450 bacteria.…

A: AIT student places 100 bacteria into a petri dish. Six hours later, he measures 450 bacteria.

Q: The production of an oil well has decreasedexponentially from 128,000 barrels per year 5 years ago…

A: The exponential equation for decay is given by :- y=Abt ...(i) , where A = initial value, b =…

Q: 1997, the population of a specific county in West Virginia was 100,000. By 2005, the population had…

A: Given query is to find exponential model.

Q: 3. Determine the exponential function that passes through the points ( 2, 8) and (-1 1)

A: Let the exponential function be: y=b·ax

Q: The population of Jefferson City is 95,000. Assuming a growth rate of 2.5% pee year, what will the…

A: Given that population of Jefferson city is P=95,000. growth rate is R=2.5% per year we have to find…

Q: In 1991 it was estimated that there were about 100 breeding pairs of Northern Spotted Owls. It was…

A: Topic: population decline

Q: A 2019 Jeep Wrangler had a new vehicle purchase price of $30,800, now has a book value of $24,500…

A: The initial price (t=0) of Jeep Wrangler in 2019 is $30,800. After 2 years, its price is $24,500.…

Q: A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium…

Q: Assume that the number of bacteria follows an exponential growth model: P(t)= P0ekt. The count in…

A: Assume that the number of bacteria follows an exponential growth model: P(t)= P0ekt. The count in…

Q: Jada is designing a study to determine whether mold grows faster in tap water or bottled water. To…

A: 1. Type of study in Jada designing: Experimental Study

Q: The initial population of pigs in a farm is 125. Given that the growth rate per year is 7.5%,…

A: Given that The initial population of pigs in a farm is 125. P0 = 125 the growth rate per year r =…

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

Assume that the number of bacteria follows an exponential growth model: P(t) = Poekt . The count in the bacteria culture was 800 after 20
minutes and 2000 after 30 minutes.
(a) What was the initial size of the culture?
(b) Find the population after 75 minutes.
(c) How many minutes after the start of the experiment will the population reach 14000?
Note: webwork usually expects four significant digits so don't round your answers.

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 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 current student population of Dallas is 1500. If the population increase at a rate of 11% each year. What will the student population be in 17 years? Write an exponential growth model for the future population (y): y = What will the population be in 17 years? (Round to nearest student)
The count in a bacteria culture was 400 after 20 minutes and 1500 after 30 minutes. Assuming the count grows exponentially,What was the initial size of the culture? Find the doubling perio? Find the population after 120 minutes? When will the population reach 11000?
The deer population in a certain area was 85 deer. They grew at a rate of 12% over 10 years. What was the deer population 10 years ago? Would this be considered geometric or exponential growth?
The answer I was given previously is not right, please help! There is a well-studied panda population in Wuyipeng. In 1989 there were 35 pandas and the researchers determined that they had an annual population growth of 1.078. (i) Which exponential model represents this population?A. (35)1.078x(35)1.078xB. 35(1.078)x35(1.078)xC. (1.078)35x(1.078)35xD. (1.078)x(1.078)x (ii) Use your model to predict how many pandas there will be in 2000.(Express your answer rounded up to the nearest panda.)Answer =
The current student population of New Orleans is 1900. If the population increase at a rate of 13% each year. What will the student population be in 7 years? Write an exponential growth model for the future population (y): y = What will the population be in 7 years? (Round to nearest student)
A painting sold for $246 in 1980 and was sold again in 1985 for $439. Assume that the growth in the value V of the collector's item was exponential. C a) Find the value k of the exponential growth rate. Assume V₂ = 246. (Round to the nearest thousandth.) b) Find the exponential growth function in terms of t, where t is the number of years since 1980. V(t) = c) Estimate the value of the painting in 2007. (Round to the nearest dollar.) d) What is the doubling time for the value of the painting to the nearest tenth of a year? years (Round to the nearest tenth.) e) Find the amount of time after which the value of the painting will be $6430. years (Round to the nearest tenth.)
Seeds found in a grave in Egypt proved to have only 58% of the Carbon-14 of living tissue. The half-life of Carbon-14 is 5730 years. When were the seeds harvested?
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…
Assume that the number of bacteria follows an exponential growth model: P(t)= P0ekt. The count in the bacteria culture was 300 after 15 minutes and 2000 after 30 minutes.Find the population after 120 minutes.
At the beginning of an experiment, there are 100 bacteria. If the bacteria follow an exponential growth pattern with a rate k = 0.002, what will the population be after 5 hours? how long will it take for the population to double?
I have submitted this question twice, and am still not getting the correct answer, please help. Atmospheric pressure decreases by about 13.3% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a given altitude in thousands of meters. Use your model to determine the atmospheric pressure at an altitude of 4700 meters.(Express your answer in millibars rounded correctly to the nearest tenth.) millibars