A company selling widgets has found that the number of items sold, x, depends upon the price, p at which30000they're sold, according the equation =(0.6p + 1)²Due to inflation and increasing health benefit costs, the company has been increasing the price by $0.03per month. Find the rate at which revenue is changing when the company is selling widgets at $3 each.Revenue is changing at a rate ofdollars per month.

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Answered: A company selling widgets has found…

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 table gives the monthly premiums for an insurance policy on people of various ages. a. Find an exponential function that models the monthly premium as a function of age. b. Find the quadratic function that is the best fit for the data. c. Graph each function with the data points to determine which model is the better fit. a. The exponential function that models the data is y= 3.059 (1.104*). (Use integers or decimals rounded to the nearest thousandth as needed for any numbers in the expression.) b. The quadratic function that models the data is y= 6.188x2-557.818x+12,448.185. (Use integers or decimals rounded to the nearest thousandth as needed for any numbers in the expression.) Age 35 40 45 50 55 Monthly Premium (S) 127 164 242 362 559 Age 60 65 70 75 Full data set Monthly Premium (S) 946 1904 3485 5873
In a particular very small region, the consumer price index, C, depends on the current value of gross regional domestic expenditure E, number of people living in poverty P, and the average number of household members in a family F, by the following formula: e-EP C = 100 + F If it is known that the gross regional domestic expenditure is decreasing at a rate of PHP 50 per year, and the number of people living in poverty and the average number of household members in a family are increasing at 3 and 1 per year, resp., how fast does the consumer price index change per year at the moment when E = 1, 000, P = 200, and F = 5?
The equation =y90001.08x describes the amount of an investment (in dollars) based on the number of years it's been allowed to grow (a) Identify what the equation y= 90001.08x illustrates. b) determine the rate at which the investment was growing by each year.
5. Someone invests $3080 in an account at 6.3% interest compounded annually. Let f(t) be the value (in dollars) of the account at t years after she invested the $3080. a) Find the equation of f. b) What will the account's value be after 12 years? (Round to the nearest cent.)
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.)
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.
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2. a. Write an exponential equation of the form y = a(b)* that passes through the points (1, 6.4) and (4, 3.2768). Explain how you got your answer OR show your work. b. Identify the percent change that is modeled by your equation in part a. In other words, identify whether your equation represents a percent increase or decrease AND how much is that percent increase or decrease.
The amount of solar power installed in the US can be modelled as M(x) = 15.45(1.46*) megawatts, where x is the number of years since 2000. This model tells us that: In 2000, there 15.45 megawatts installed, and the amount is growing by 146% per year In 2000, there were 15.45 megawatts installed, and the amount is growing by 46% per year In 2000, there were 1.46 megawatts installed, and the amount is growing by 1545% per year In 2000, there were 1.46 megawatts installed, and the amount is growing by 15.45% per year.
33. A family invested $2,000 into an account that pays 2% interest compounded annually. In the functions below, x = time in years and y = total amount in the account after x years. %3D y= 40x +2,000 y = 2,000(1.02) Use the function that models the situation correctly. To the nearest dollar, how much money is in the family's account after 5 years? A. $2,081 В. $2,200 C. $2,208 D. $10,200 E34-3 F7 FB & 4 7 8 T Y U F G H J K C V B NM 立 LU
1/x +3/2 = -4/7 + 6/(2 x) %3D

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