3. The gross national product (GNP) represents the sum of consumption purchases of goodsand services, government purchases of goods and services, and gross private investment(which is the increase in inventories plus buildings constructed and equipment acquired).Assume that the GNP is increasing at the rate of 3% per year and that the national debtis increasing at a rate proportional to the GNP.a. Construct a system for two ordinary differential equations modeling the GNP andnational debt.b. Solve the system in part (a), assuming the GNP is Mo and the national debt is No atyear 0.c. Does the national debt eventually outstrip the GNP? Consider the ratio of the nationaldebt to the GNP.

We solve the problem regarding GNP and national debt

Answered: 3. The gross national product (GNP)…

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...

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tion 18 Find the producers' surplus for the supply curve p = 0.02x + 7 at x = 100. $800 $100 O $200 O $900 • Previous
Assume that you can contribute $7,000 per year into a retirement fund that grows at a constant rate of 7% per year. (a) Write a first-order linear differential equation that models your retirement savings. (b) find the total amount saved after 10 years. (c) assume that instead of contributing $7,000 per year, you were able to increase your contribution by $50 each year ($7,000 first year, $7,050 second year, etc.). How much money would you have saved after 10 years?
An investor is presented with a choice of two investments: an established clothing store and a new bookstore. Each choice requires the same initial investment and each produces a continuous income stream of 3%, compounded continuously. The rate of flow of income from the clothing store is f(t)=12,000, and the rate of flow of income from the book store is expected to be g(t)=10,000e^0.05t. Compare the future values of these investments to determine which is the better choice over the next 2 years.
(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.
23. A population grows according to the logistic growth model, with growth parameter r = 0.8. Starting with an initial population given by po = 0.3, a) Find p₁ (report your answer to 4 decimal places) = 0.168 b) Find p2 (report your answer to 4 decimal places) = 0.1128 X c) Determine what percent of the habitat's carrying capacity is taken up by the 3rd generation. (Report your answer to 2 decimal places) 0.08 X %
Please answer this question using the assumptions from the Solow Model In a country, the production function in terms of output per capita, y, and capital per labor, k, is y = k(12) The fraction of output saved, s, is 25% and the depreciation rate, δ, is 0.05. Assume that the population does not grow. What is the steady-state of capital per worker, k*, and output per worker, y*? What happens to the steady-state values if the population growth rate rises to 5%? By how much would the country have to increase its savings rate in b) in order to reach the same levels of steady-state values as in a)? Does the country’s growth rate increase in c) compared to a)? how?

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