HW Q10 Population Growth A major corporation is building a 4,325 acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As aresult of this development, the planners have estimated that Glen Clove's population (in thousands) t years from now will be given by the following function.P(t)=45t² + 125t + 300t² + 2t + 60(a) What is the current population (in number of people) of Glen Cove?people(b) What will be the population (in number of people) in the long run?people

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Answered: Population Growth A major corporation…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.1: Exponential Functions And Their Graphs

Problem 61E: Population Growth The projected population of the United States for the years 2025 through 2055 can...

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Concentration of a Mixture A 1000-liter tank contains 50 liters of a 25brine solution. You add xliters of a 75brine solution to the tank. (a) Show that the concentration C, the proportion of brine to total solution, in the final mixture is C=3x+504(x+50). (b) Determine the domain of the function based on the physical constraints of the problem. (c) Sketch the graph of the concentration function. (d) As the tank is filled, what happens to the rate at which the concentration of brine is increasing? What percent does the concentration of brine appear to approach?
Drug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?
Weekly Cost: The weekly cost of running a small firm is a function of the number of employees. Every week there is a fixed cost of 2500, and each employee costs the firm 350. For example, if there are 10 employees, then the weekly cost is 2500+35010=6000dollars. a. What is the weekly cost if there are 3 employees? b. Find a formula for the weekly cost as a function of the number of employees. You need to choose variable and function names. Be sure to state units. c. Make a graph of the weekly cost as a function of the number of employees include values of the variable up to 10 employees. d. For what number of employees will the weekly cost be 4250?
Geometry The perimeter of a rectangle is 200meters. (a) Draw a diagram that gives a visual representation of the problem. Let x and y represent the length and width of the rectangle, respectively. (b) Write yas a function of x.Use the result to write the area A as a function of x. (c) Of all possible rectangles with perimeters of 200meters, find the dimensions of the one with the maximum area.
Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?
Stadium Revenue A baseball team plays in a stadium that holds 55.000 spectators. With the ticket price at $10, the average attendance at recent games has been 27,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. (a) find a function that models the revenue in terms of ticket (b) find the price that maximizes revenue from ticket sales. (c) What ticket Bice is so high that no revenue is generated?
Population Growth The projected population of the United States for the years 2025 through 2055 can be modeled by P=307.58e0.0052t, where P is the population (in millions) and t is the time (in years), with t=25 corresponding to 2025. (Source: U.S. Census Bureau) (a) Use a graphing utility to graph the function for the years 2025 through 2055. (b) Use the table feature of the graphing utility to create a table of values for the same time period as in part (a). (c) According to the model, during what year will the population of the United States exceed 430 million?
Population Growth The projected population of the United States for the years 2025 through 2055 can be modeled by P=307.58e0.0052t, where P is the population (in millions) and t is the time (in years), with t=25 corresponding to 2025. (a) Use a graphing utility to graph the function for the years 2025 through 2055. (b) Use the table feature of the graphing utility to create a table of values for the same time period as in part (a). (c) According to the model, during what year will the population of the United States exceed 430 million?
Planet Growth The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall. For a pasture in the arid zone of Australia the formula Y=55.120.01535N0.00056N2+3.946R gives an approximation of the growth. Here R is the amount of rainfall, in millimeters, over a 3 month period; N is the plant biomass, in kilograms per hectare, at the beginning of that period; and Y is the growth, in kilograms per hectare, of the biomass over that period. For comparison, 100 millimeters is about 3.9 inches, and 100 kilograms per hectare is about 89 pounds per acre. For this exercise, assume that the amount of plant biomass initially present is 400 kilograms per hectare, so N=400. a. Find a formula for the growth Y as a function of the amount R of rainfall. b. Make a graph of Y versus r. Include values of R from 40 to 160 millimeters. c. What happens to Y as R increases? Explain your answer in practical terms. d. How much growth will there be over a 3 month period if initially there are 400 kilograms per hectare of plant biomass and the amount of rainfall is 100 millimeters?

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