Question

In: Math

In 2010, (when t = 0), the population of a country was 1.16 billion people and...

In 2010, (when t = 0), the population of a country was 1.16 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years since 2010, the constant of proportionality is 0.0138.

(a) Define the variables.

Let P be the population, in trillions of people, in year t, where t represents the number of years before 2010.

Let P be the population, in billions of people, in year t, where t represents the number of years before 2010.    

Let P be the population, in billions of people, in year t, where t represents the number of years since 2010.Let P be the population, in billions of people, in month t, where t represents the number of years before 2010.

Let P be the population, in billions of people, in year t, where t represents the current year.


(b) Write a differential equation to describe the relationship.

dP
dt

=

with initial condition P(0) = _____________

(c) Solve the differential equation.
P = _________________________

Solutions

Expert Solution


Related Solutions

A country reported a nominal GDP of $115 billion in 2010 and $125 billion in 2009...
A country reported a nominal GDP of $115 billion in 2010 and $125 billion in 2009 and reported a GDP deflator of 85 in 2010 and 100 in 2009. What happened to real output and prices from 2014 to 2015? Please explain.
In 2010, a country imported goods worth $500 billion and exported goods worth $443 billion. It...
In 2010, a country imported goods worth $500 billion and exported goods worth $443 billion. It exported services worth $248 billion and imported services worth $330 billion. Payments on investments abroad totaled $199 billion, while returns paid on foreign investments were $125 billion. Unilateral transfers from the country to other nations amounted to $94 billion. What was the country’s current account deficit for 2010? A. $70 billion B. $159 billion C. $142 billion D. $65 billion
A Population Model The population of the world in 2013 was 7.13 billion people and was...
A Population Model The population of the world in 2013 was 7.13 billion people and was growing at a rate of 1.1% per year. Assuming that this growth rate continues, the model P(t) = 7.1311.0112^(t-2013) represents the population P (in billions of people) in year t. (a) According to this model, when will the population of the world be 10 billion people? (b) According to this model, when will the population of the world be 12.2 billion people?
The world population in 1999 was approximately P0 = 6.067 billion people, and in 2000, it...
The world population in 1999 was approximately P0 = 6.067 billion people, and in 2000, it was approximately P1 = 6.145 billion people. Logistic Growth Model. Scientists often use a different function to model population growth when there are limited resources, as is the case with our planet. To do this, we will model the world population (in billions of people) in year t by the function L(t) = P0K / P0 + (K − P0)e-rbt , where P0 and...
The total world population in the year 1800 was 1 billion people. Today there are 7.8...
The total world population in the year 1800 was 1 billion people. Today there are 7.8 billion people in the world. Year Global Population (in billions) 2017 7.511 2018 7.594 2019 7.700 2020 7.800 (a) Using the table above calculate the average population growth rate over the past 3 years. (b) Using the growth rate from part (a), calculate in what year the world population will reach 9 billion people (round down to the nearest year). (c) List 3 stresses...
In 2015, the world population was estimated at approximately 8.4 billion people. Also in 2015, the...
In 2015, the world population was estimated at approximately 8.4 billion people. Also in 2015, the annual per capita gross domestic product (GDP) was approximately $9,350, and approximately 0.38 W-year of energy was expended per dollar of GDP. The world population is projected to be approximately 10 billion by 2050. Assuming the world’s standard of living increases by 1.6% per year and energy efficiency increases by 1% per year, how much power will the world consume by 2050 in TW?...
Country A has a population of ?(?) = 75(0.83) ? where t is the number of...
Country A has a population of ?(?) = 75(0.83) ? where t is the number of years after 2000 and ?(?) is the population of country A in millions of people. Country B has a population of ?(?) = 20(1.2) ? where t is the number of years after 2000 and ?(?) is the population of country B in millions of people. (a) Graph both functions on the same axis for the years 2000 through 2010. (b) What was the...
Consider a country with a population of 10: 5 blue people and 5 green people. Each...
Consider a country with a population of 10: 5 blue people and 5 green people. Each green person has an income of $1 per year. Each blue person has an income of $3 per year. (a) Draw the Lorenz curve for this country. (b) On your diagram for part (a), indicate clearly what area you would divide by what other area to calculate the Gini coefficient. (c) Calculate the Gini coefficient. [Hint: the easiest way to do this is to...
At the end of 2012, global population was about 7.0 billion people. What mass of glucose...
At the end of 2012, global population was about 7.0 billion people. What mass of glucose in kg would be needed to provide 1500 cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to CO2(g) and H2O(l) according to the following thermochemical equation: C6H12O6(s)+6O2(g)⟶6CO2(g)+6H2O(l) ΔH∘=−2803kJ
Show that when T – t becomes 0, the Black and Scholes call price become max{0,...
Show that when T – t becomes 0, the Black and Scholes call price become max{0, S – K}  
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT