Population Models
Population models play a pivotal role in understanding and predicting demographic trends, aiding in the formulation of informed policies and strategies. These mathematical frameworks analyze the dynamics of populations, considering factors such as birth rates, death rates, and migration patterns. By employing statistical techniques, population models provide valuable insights into population growth, age distribution, and overall dynamics. These models serve as indispensable tools for governments, researchers, and policymakers seeking to make data-driven decisions in areas ranging from healthcare planning to resource allocation.
Questions
- A population of grasshoppers quadruples in twenty days. Assuming exponential growth, if the present population is 40 million, what will it be in 50 days? Answer the question by first finding the number y of grasshoppers as a function of time t (in days)?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (0,4) and (5, 1/2)?
- 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)#?
- What is described by the exponential model of population growth?
- 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 I work with the exponential model #y = ae^(kt)#?
- 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?
- 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?
- 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.
- 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?
- 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?
- How do you find the exponential model #y=ae^(bx)# that goes through the points (0,1) and (3,10)?
- 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?
- What is the major assumption of the exponential model of population growth?