In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of a 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 the difference between this limit and the current sales level. For example, if we expect sales to grow to 5 thousand dollars in the long run, then 5- s gives the unattained sales. The model states that the growth rate G is proportional to the product of the sales levels and the unattained sales. Assume that the constant of proportionality is 0.7 and that the sales grow to 4 thousand dollars in the long run. (a) Find a formula for unattained sales. (b) Write an equation that shows the proportionality relation for G. G= (c) On the basis of the equation from part (b), make the graph of G as a function of s. 3- G 2 1 3 G 2 1

In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of a 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 the difference between this limit and the current sales level. For example, if we expect sales to grow to 5 thousand dollars in the long run, then 5- s gives the unattained sales. The model states that the growth rate G is proportional to the product of the sales levels and the unattained sales. Assume that the constant of proportionality is 0.7 and that the sales grow to 4 thousand dollars in the long run. (a) Find a formula for unattained sales. (b) Write an equation that shows the proportionality relation for G. G= (c) On the basis of the equation from part (b), make the graph of G as a function of s. 3- G 2 1 3 G 2 1

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

Y = AK®N1- e = 1/4. In a year in the Consider an economy with the production function with capital stock grew at rate 9.5%, the population grew at 3.9%, and productivity grew at 6.6%, what is the growth rate of Y? (Note: provide answer as a percent growth rate with one decimal figure)
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1600 fish. Absent constraints, the population would grow by 230% per year.
Think back to early in the semester when the weather was cold and often snowy. Imagine that in a parking lot near campus, it snowed quite a bit and the snow was plowed into one giant mound in the corner of the parking lot. The mound was 24 inches high, and it’s base was 36 inches wide. After that day, it warmed up and the mound started melting such that it’s height was decreasing at a rate of 0.5 inches per hour, and the sides of the base were decreasing at a rate of 0.25 inches per hour. (a) Find the rate at which the entire mound of snow was melting, i.e. the rate at which the volume of the mound was decreasing. (V = 1/3 lwh where l is the length of the base, w is the width of the base, and h is the height of the pyramid) (b) How many hours will it take for the mound of snow to be gone?
Q1. Complete the Table: Growth Rate Compounding Growth factor Frequency P.V. F.V. £ 4% for each of 10years 4% for each of 10years r for T years 10% 1000 Annual P Semi-annual continuous annual 805.26 4% for 3 years and 5% for 2 100(1.04) (1.05) years 5% for T years. 100 continuous 128.40 5) The departure time of the 9:15 train from Kings Cross to Cambridge is claimed by the Service Providers to be on average within the 3 minute delay time allowed. A group of commuters collected a sample of 100 departure times, d and obtained the following data: Sample mean of delayed time, d = 4.6; sample variance, s = 6.25. Can the claim that the delay time is above the 3 minutes delay time allowed be accepted at the 5% significance level?
Is y = 3(x-1) + 4 an increasing or a decreasingfunction?
K The manufacturer's suggested retail price (MSRP) for a particular car is $25,275, and it is expected to be worth $14,427 in 4 years. (a) Find a linear depreciation function for this car. (b) Estimate the value of the car 5 years from now. (c) At what rate is the car depreciating? (a) What is the linear depreciation function for this car? f(x) = (Simplify your answer. Do not include the $ symbol in your answer.) (b) What is the estimated value of the car 5 years from now? (c) At what rate is the car depreciating? The car is decreasing in value an average of $ a year.
A client’s orders are growing consistently at x% per year. A) If three years from now orders are 50% higher than today, what is the annual growth rate (x)? B) Write an expression (in terms of x) for how many years it will take until orders are double what they are currently