Population Models

Key Questions

• What is the definition of population dynamics?

  Population dynamics is a subject under the broader study of dynamic systems. This is studied under life sciences that studies the size and age composition of populations.

  That includes human populations or even populations of bacteria, or just any other organism.

  Aritra G. · 6 · Mar 27 2017
• What is described by the exponential model of population growth?

  Answer:

  Exponential model of population growth describes the volume of population (number of species) as an exponential function of time similar to:
  #P=a*b^(c*T)#
  where #a,b,c# - are constants, #T# - time.

  Explanation:

  Imagine you have bacteria that divides into 2 every hour.
  If at #T=0# we have one such bacteria, at #T=1# (in an hour) we will have two of them, at #T=2# (in two hours) we will have 4 of them etc.
  At any time #T# we will have the number of bacteria equal to
  #P=2^T#

  The above is a typical exponential growth of a population. The number of off-springs and other parameters can modify the formula, but it still will be based on exponential function with the time parameter in the exponent.

  Obviously, real life conditions introduce complications in the formula based on variable productiveness and mortality rates.

  Zor Shekhtman · 1 · Feb 2 2016

• What is described by the exponential model of population growth?
• What is the major assumption of the exponential model of population growth?
• What is the definition of population dynamics?
• How do I work with the exponential model #y = ae^(kt)#?
• A exponential model #A=24.7e^(.03t)# describes the population, A(in millions), of a country's years after 2003, how do you find the population in 2010?
• How do you graph #y = 2(0.5)^x#?
• How do you find the exponential model #y=ae^(bx)# that goes through the points (0,1) and (3,10)?
• How do you find the exponential model #y=ae^(bx)# that goes through the points (0,4) and (5, 1/2)?
• Use the exponential growth model #P(t) = P_0e^(kt)#. How long will it take for the population of a certain country to double if its annual growth rate is 3.5%?
• Use the exponential growth model #P(t) = P_0e^(kt)#. The half-life of thorium-229 is 7,340 years. How long will it take for a sample of this substance to decay to 20% of its original amount?
• A bacteria culture starts with 1000 bacteria. 2 hours later there are 1500 bacteria. How do you fin an exponential model for the size of the culture as function of time t in hours, and use the model to predict how many bacteria there will be after 2 days?
• How do you write an exponential function to model the situation. then predict the value of the function after 5 years (to the nearest whole number). A population of 430 animals that decreases at an annual rate of 12%?
• A population of bacteria is growing according to the exponential model #P = 100e^(70t)#, where P is the number of colonies and t is measured in hours. How many colonies are present initially?
• Using #P(t)=P_oe^(kt)# how do you find the count in the bacteria culture was 900 after 20 minutes and 1100 after 35 minutes and find what was the inital size of the culture and the population after 95 minutes?
• Five years ago, you purchased a riding lawn mower for $1600. Recently, you resold the mower for $525. Assume that the value of the mower decays exponentially with time. How do you write an exponential decay model?
• A baseball card bought for $50 increases in value by 3% each year. How do you write an exponential function to model its value. Then find its value after 5 years?
• The level of thorium in a sample decreases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of its original thorium remaining. How old is the meteorite?
• Assume that the number of bacteria follows an exponential growth model P(t)=Pe^{kt}? The count in the bacteria culture was 500 after 15 minutes and 2000 after 40 minutes. What was the initial size of the culture?
• An initial population of 295 quail increases at an annual rate of 7%. Write an exponential function to model the quail population. What will the approximate population be after 2 years?
• A bacteria culture starts with 500 bacteria and doubles in size every 6 hours. How do you find an exponential model for t?
• A bacteria culture starts with 500 bacteria and doubles in size every 3 hours. How do you find an exponential model for t?
• How do you write an exponential function to model the situation, then find the value of the function after 5 years to the nearest whole number. A population of 200 people that decreases at an annual rate of 6%?
• A bacteria culture has an initial population of 10,000. If it's initial population declines to 6,000 in 8 hours, what will it be at the end of 10 hours? Assume that population decreases according to the exponential model.
• A new flu virus is introduced when a stranger visits an isolated village of 8000 people. Every infected person infects two more each day. How do you write an exponential function to model the number of UNINFECTED people?
• In 1950 the world’s population was approximately 2.56 billion and was growing at a rate of about 1.47% Assume the growth rate continues. How do you write an exponential equation that models the world’s population, P for n years after 1950?
• The population of Silver Run in the year 1890 was 6250. Assume the population increased at a rate of 2.75% per year. How do you estimate the population in 1915 and 1940?
• How long, to the nearest year, will it take an investment to triple if it is continuously compounded at 6% per year?
• An initial population of 175 quail increases at an annual rate of 22%. Write an exponential function to model the quail population. What will the approximate population be after 5 years?
• The bat population in a certain Midwestern county was 230,000 in 2009, and the observed doubling time for the population is 22 years. How do you find an exponential model?
• A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 13,000. What was the initial size of the bird population?
• The half-life of sodium-24 is 14.9h. A medical facility buys a 50mg sample. How do you determine the exponential function that models the amount, A(t), of sodium-24 that will be present in the sample after t hours?
• How do you write an exponential function to model the situation. Then estimate the value of the function after 5 years. A population of 290 animals that increases at an annual rate of 9%?
• A large city is growing by at rate of 0.8% annually. If there were 3,390,000 residents of the city in 1992, predict how many will be living in the city in 1997?
• You deposit $2500 in an account that pays 3% annual interest compounded continuously. What is the balance in your account after 4 years?
• If the population of the world was 6.5 billion in 2006 and is currently 7.1 billion (in the year 2013), what will the population be in the year 2050?
• How do you write the exponential growth function to model the following situation: A population of 422,000 increases by 12% each year?
• The number of bacteria in a culture grew from 275 to 1135 in three hours. How do you find the number of bacteria after 7 hours and Use the exponential growth model: #A = A_0e^(rt)#?
• There were 35 million people in 1980 (when t=0 ) and 80 million people in 1990. How do you find an exponential model for the population (in millions of people) at any time t, in years after 1980?
• A colony of bacteria grows according to the law of uninhibited growth. If 100 grams of bacteria are present initially and 250 grams are present after two hours, how many will be present after 4 hours?
• How do you find the associated exponential growth model: Q = 3,000 when t = 0; doubling time = 3?
• Suppose that the sales at Borders bookstores went from 78 million dollars in 1990 to 424 million dollars in 1992. How do you find an exponential function to model the sales (in millions of dollars) as a function of years, t, since 1990?
• A sample of 2000 bacteria selected from this population reached the size of 2266 bacteria in five hours. How do you find the continuous growth rate per hour?
• The yearly capita consumption of whole milk in the US reached a peak of 40 gallons in 1945. It has been steadily decreasing at a rate of about 2.8% per year. How do you find an exponential model M(t) for capita whole milk consumption?
• If the population of the world was 6.5 billion in 2006 and is currently 7.1 billion (in the year 2013), what will the population be in the year 2050?
• Question #b13c2
• Which country has a decreasing population? By what percentage us the population of that country decreasing each year?
• 1(a). How much will #€5000# will become, if they are invested for #7# years at #4.5%# per annum compounded every month? (b). If an amount #€7000#, invested for #10# years compounded every year doubles, at what rate was it invested?