An economist is interested in how the price of a certain item affects its sales. When the price ofthe item is $ p, the number of items sold will be q = f(p). (This is the idea of "demand")Suppose we found out that f(150) = 2,000 and that f'(150) = -25.(a) Sketch the information of two boldfacestatements in a quick picture/sketch:(b) Write out in words what the first statement f(150) = 2,000 means in the context.(c) The fact that the derivative is negative reflects what natural phenomenon?(d) Write out in words what the statement f'(150) = -25 means in the context.(Add in appropriate units!)(e) Use the information given to estimate f(151) and f(149.5).Show your work, and explain your rationale for proceeding as you did.A little picture would be ideal to explain your thinking.

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Answered: An economist is interested in how the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following two functions have a common input, year t: R gives the average price, in dollars, of a gallon of regular unleaded gasoline, and P gives the purchasing power of the dollar as measured by consumer prices based on 2010 dollars. (a) Using function notation, show how to combine the two functions to create a new function giving the price of gasoline in constant 2010 dollars R(tdollars gallon (RP(t dollars gallon 2010 dollars P(t) dollars (at pump) R(t) dollars. P(tdollars (at pump) 2010 dollars (R P)(t) 2010 dollars gallon gallon Rit dollars . Pt dollars (at pump) 2010 dollars (R P(t dollars gallon gallon OR(t) dollars gallon 2010 dollars P(t) 2010 dollars gallon P(t) dollars (at pump) (R OR(t)dollars gallon 2010 dollars P(t) dollars (at pump) = (R + P)(t 2010 dollars gallon (b) What are the output units of the new function? O2010 dollars per gallon Odollars per gallon gallons per dollar 2010 dollars per dollar (at pump) Ogallons per 2010 dollar
Find the standard matrix of a linear 3 transformation T : R R' that rotates each vector counterclockwise (CW) about the positive x- axis by an angle of 3' followed by a reflection about the xz- plane, followed by dilation with a factor 4.
A city's population was 28,500 people in the year 2015 and is growing by 950 people a year.(a) Give a formula for the city’s population, P, as a function of the number of years, t, since 2015. Do not use commas in your submitted answer. P= people. (b) What is the population predicted to be in 2020? P= people. (c) When is the population expected to reach 35,000? Round your answer to the nearest integer. The population will reach 35,000 in the year.
Suppose D defines the number of miligrams of drug concentration that is present in the blood stream of certain patient after h hours of injection which is modeled by the function D(h)=4e-0.3(h), then determine the number of milligram of drug that must be present after 3 and 9 hours
How can the One-to-One Functions Graphically be identified?
The Lacledge Gas Company in St. Louis, Missouri in the winter of 2012–2013 charged customers $21.32 per month plus $1.19071 per therm for the first 30 therms of gas used and $.57903 for each therm above 30. (a) How much revenue does the company get from a customer who uses exactly 30 therms of gas in a month? (b) Find the rule of the function R(x) that gives the company's monthly revenue from one customer, where x is the number of therms of gas used. (Hint: R(x) is a piecewise-defined function that has a two-part rule, one part for x 30.)
The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)
This might be a long question, so I'll separate it as (a), (b) and so on. If you can find the indicated composite function and its domain for the following. The equation is sent in the picture. (a) (f o g) (x) = and the domain for it. (b) (g o f) (x) = and the domain for it. (c) (f o f) (x) = and the domain for it. (d) (g o g) (x) = and the domain for it.
2. Lijah opened an account at Advantis Credit Union. The balance of her account after x years is represented by the function b(x) = 500(1.05)*. What annual interest rate is Lijah earning? а. b. After how many years did it take for Lijah's balance to double? Show all of your work.
3. An open box is formed by cutting a square piece out of each corner of a 10-by-8 inch metal plate, as shown in the picture below. We denote the length of the side of these square pieces, measured in inches, by x. X 10 a. Determine the equation of the function which expresses how the volume V of this box depends on x. b. Find the domain of the function V(x).
Suppose soda is on sale for $0.50 a can, and you have a coupon for $0.80 off your total purchase. Write a function rule for the cost of n cans of soda. A)c(n)=0.80n-0.50 B)c(n)=0.50n-0.80 C)c(n)=(0.50+n)-0.80 D)c(n)=(0.80+n)-0.50

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