The rate of growth dP/dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 8
The rate of growth dP/dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 8, where P is the population size and t is the time in days (0≤ t ≤ 10). The initial size of the population is 200. Approximate the population after 7 days. Round the answer to the nearest integer.
Homework Answers
Add Answer to:
The rate of growth dP/dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 8
The rate of change of the population of a small town is dP/dt = kP
The rate of change of the population of a small town is dP/dt = kP, where P is the population, t is time in years and k is the growth rate. If P = 20000 when t = 3 and P = 30000 when t = 4, what is the population when t= 10? Round your answer to the nearest integer.
The growth rate of a particular bacteria is modeled by the differential equation dP/dt = k P. Suppose a population at...
The growth rate of a particular bacteria is modeled by the differential equation dP/dt = k P. Suppose a population at of bacteria doubles in size every 11 hours. Initially, there are 200 bacteria cells. If we begin growing the bacteria for our experiment at 7: 00pm on September 4, when is the earliest the necessary 5,000,000 bacteria cells will be ready? a) September 07 at 12: 00pm b) September 07 at 9: 00pm c) September 08 at 8: 00am...
2. The growth rate of a population of bacteria is directly proportional to the population p()...
2. The growth rate of a population of bacteria is directly proportional to the population p() (measured in millions) at time t (measured in hours). (a) Model this situation using a differential equation. (b) Find the general solution to the differential equation (c) If the number of bacteria in the culture grew from p(0) = 200 to p(24) = 800 in 24 hours, what was the population after the first 12 hours?
The growth rate of a particular bacteria is modeled by the dP differential equation 17 =...
The growth rate of a particular bacteria is modeled by the dP differential equation 17 = k P. Suppose a population dt of bacteria triples in size every 11 hours. Initially, there are 100 bacteria cells. If we begin growing the bacteria for our experiment at 8:00am on January 4, when is the earliest the necessary 5,000,000 bacteria cells will be ready?
18. [-15 Points] DETAILS LARCALCET7 5.7.091.MI. MY NOTES ASK YOU A population of bacteria P is...
18. [-15 Points] DETAILS LARCALCET7 5.7.091.MI. MY NOTES ASK YOU A population of bacteria P is changing at a rate based on the function given below, where t is time in days. The initial population (when t = 0) is 1100. dp dt = 3100 1 + 0.25t (a) Write an equation that gives the population at any time t. P(t) = (b) Find the population when t = 2 days. (Round your answer to the nearest whole number.) P(2)...
Part B Please!! Scenario The population of fish in a fishery has a growth rate that...
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
3. (17 points) The growth in a population of bacteria follows a logistic growth model given...
3. (17 points) The growth in a population of bacteria follows a logistic growth model given by the differential equation dP 0.05P - 0.00001p? dt with units of number of bacteria and hours. (a) (3 points) What is the carrying capacity of this population? (b) (9 points) Given an initial population of 1000 bacteria, how long will it take for the population to double? (c) (5 points) What is the rate of change (per hour) in the size of the...
&7 4. A population P grows at a constant rate of a organisms per unit time, and the death rate is proportional...
&7 4. A population P grows at a constant rate of a organisms per unit time, and the death rate is proportional to the population size with the proportionality constant k. A. Assume the initial population P(0) Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answe terms Po, a, k and a constant C.) wer must contain the...
Suppose that the rate of change of a population is given by: dP dt = kP(M-P) a) What model of pop...
Suppose that the rate of change of a population is given by: dP dt = kP(M-P) a) What model of population growth is this ? b) What does it predict for the growth of the population as the population increases ? c) Sketch what happens to the population if the initial population, Po, were such that G) 0< Po< M/2, (ii) M/2 < PoM and (iii) Po > M (all on the same graph of population as a function of...
This exercise uses the population growth model. The count in a culture of bacteria was 400...
This exercise uses the population growth model. The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. (a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your answer to the nearest whole number.) 104 % (b) What was the initial size of the culture? (Round your answer to the nearest whole number.) 200 x bacteria (c) Find a function that models the number...
The growth rate of a particular bacteria is modeled by the differential equation dP/dt = k P. Suppose a population at of bacteria doubles in size every 11 hours. Initially, there are 200 bacteria cells. If we begin growing the bacteria for our experiment at 7: 00pm on September 4, when is the earliest the necessary 5,000,000 bacteria cells will be ready? a) September 07 at 12: 00pm b) September 07 at 9: 00pm c) September 08 at 8: 00am...
2. The growth rate of a population of bacteria is directly proportional to the population p() (measured in millions) at time t (measured in hours). (a) Model this situation using a differential equation. (b) Find the general solution to the differential equation (c) If the number of bacteria in the culture grew from p(0) = 200 to p(24) = 800 in 24 hours, what was the population after the first 12 hours?
The growth rate of a particular bacteria is modeled by the dP differential equation 17 = k P. Suppose a population dt of bacteria triples in size every 11 hours. Initially, there are 100 bacteria cells. If we begin growing the bacteria for our experiment at 8:00am on January 4, when is the earliest the necessary 5,000,000 bacteria cells will be ready?
18. [-15 Points] DETAILS LARCALCET7 5.7.091.MI. MY NOTES ASK YOU A population of bacteria P is changing at a rate based on the function given below, where t is time in days. The initial population (when t = 0) is 1100. dp dt = 3100 1 + 0.25t (a) Write an equation that gives the population at any time t. P(t) = (b) Find the population when t = 2 days. (Round your answer to the nearest whole number.) P(2)...
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
3. (17 points) The growth in a population of bacteria follows a logistic growth model given by the differential equation dP 0.05P - 0.00001p? dt with units of number of bacteria and hours. (a) (3 points) What is the carrying capacity of this population? (b) (9 points) Given an initial population of 1000 bacteria, how long will it take for the population to double? (c) (5 points) What is the rate of change (per hour) in the size of the...
&7 4. A population P grows at a constant rate of a organisms per unit time, and the death rate is proportional to the population size with the proportionality constant k. A. Assume the initial population P(0) Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answe terms Po, a, k and a constant C.) wer must contain the...
Suppose that the rate of change of a population is given by: dP dt = kP(M-P) a) What model of population growth is this ? b) What does it predict for the growth of the population as the population increases ? c) Sketch what happens to the population if the initial population, Po, were such that G) 0< Po< M/2, (ii) M/2 < PoM and (iii) Po > M (all on the same graph of population as a function of...
This exercise uses the population growth model. The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. (a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your answer to the nearest whole number.) 104 % (b) What was the initial size of the culture? (Round your answer to the nearest whole number.) 200 x bacteria (c) Find a function that models the number...
Most questions answered within 3 hours.
-
Assume memory access is 10 units of time and disk access is
10000 units of time....
asked 2 minutes ago -
1. Are all good samples random?
2. Magazines often report surveys giving statistics such as “63%...
asked 23 minutes ago -
Under all the various types of market structures, firms
must eventually earn some economic profits for...
asked 10 minutes ago -
Consider the following fitness regime for a single locus trait
with two co-dominant alleles: w11 =...
asked 15 minutes ago -
A large cable company reports the following.
80% of its customers subscribe to its cable TV...
asked 30 minutes ago -
Please answer the question in brief.
Discuss the role of ERP in organizations. Are ERP tools...
asked 16 minutes ago -
Discuss the pros and cons of collaborative software such
as SameTime. Does it increase productivity? What...
asked 28 minutes ago -
Buying your in-laws a gift because it’s expected is
due to the ____________ motive of gift-giving....
asked 31 minutes ago -
Calculate the expected value, the variance, and the standard
deviation of the given random variable X....
asked 1 hour ago -
A hospital performs 100 surgeries per week. The probability that
complications after surgery occur is 10%....
asked 1 hour ago -
1 point) Given the significance level α=0.01 find the following:
(a) left-tailed z value z= (b)...
asked 1 hour ago -
Assuming you are the head of the software development unit at
Cyber.Soft, explain and justify why...
asked 39 minutes ago