The following table shows the number, in millions, graduating from high school in the United States in the given year.t After 1992, the number of high school graduates has increased each year.Year Number graduating (in millions)19852.8319872.6519892.4719912.29(a) By calculating differences, show that these data can be modeled using a linear function. (Let d be years since 1985 and N the number of graduating high school students, in millions.)1985 to 19871987 to 19891989 to 1991✓✓x✓XXChange in dChange in N20.18(b) What is the slope for the linear function modeling high school graduations? (Round your answer to two decimal places.)-0.09✔million per year.Explain in practical terms the meaning of the slope.This means that each year fewer✔✔ high school students graduated.Calculate that value.2.2(c) Find a formula for a linear function that models these data. (Let d be years since 1985 and N the number of graduating high school students, in millions.)N = -0.09d + 181.48Need Help?20.18(d) Express, using functional notation, the number graduating from high school in 1992.N( 1992x )millionRead It20.18XMaster It

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Answered: The following table shows the number,…

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 follow table shows total dollar sales (in thousands) for a local retailer for various years. Year 2019 2020 2021 2022 2023 Sales ($) 16 21 26 31 36 a) What was the dollar amount of sales for 2022? $ b) By how much did sales increase each year? $ c) Find a linear function S(x) that models the above data, where x is the number of years after 2018 (so that the year 2019 corresponds to x = 1, the year 2020 corresponds to x = 2, and so on) and S(x) is the dollar amount of sales in thousands. S(x) = X + d) Use S(x) to predict sales in 2025. $ If needed, round answer to 5 decimal plates. Enter DNE for Does Not Exist, oo for Infinity Question Help: Message instructor Submit Question thousand thousand thousand
The number of cells in a blue container doubles each day. The number of cells in a red container each day is shown in the table below. Day Number of Cells 1 50 75 100 125 150 175 7 200 A scientist creates functions to model the cell growth in both containers. Which statement about the functions is true? A.O The function for the blue container is linear, and the function for the red container is non-linear. B.O The functions for both containers are linear. C.O The function for the blue container is non-linear, and the function for the red container is linear. D.O The functions for both containers are non-linear. Copyright 20
An economist is studying the median yearly income of workers by their ages. Age (yr) 18 28 38 48 58 68 Median Income ($) 17,480 30,650 37,440 41,230 37,570 21,390 a. What function best models the data (linear, quadratic, exponential)? b. Write a function that models the data. c. Use your model to predit the median income for a worker who is 43 years old. Round to the nearest dollar.
The graphs show the various temperatures for the month of January in 2 cities. Which city has a higher variability of their January temperature?
The height y (in meters) of a volcano in the southeast Pacific Ocean is recorded in the table for selected years since 1960. Number of Years Since Height (m)| 1960, x 166 10 290 20 408 30 526 40 650 50 760 54 813 a. Graph the data in a scatter plot. b. Use the points (0, 166) and (40, 650) to write a linear function that defines the height y of the volcano, x years since 1960. c. Interpret the meaning of the slope in the context of this problem. d. Use the model in part (b) to predict the height of the volcano in the year 2030 assuming that the linear trend continues.
(a) The number of tourists visiting a certain country is a linear function of time. Using this fact, fill in the blanks in the following table. Be sure to show your work. Date N: number of tourists (in thousands) 1979 103 1983 91.8 1987 80.6 1991 1995 (b) Find a formula for a linear function that models the data in the table (N as a function of t, the number of years since 1979.) N = t + (c) Explain in practical terms the meaning of the slope of the function you found in Part (b). O The rate at which a tourist visits the country every year O The number of years since the last visit of the tourists O The number of tourists visiting the country on a given year O The rate at which the number of tourists is decreasing every year (d) Use your formula from Part (b) to predict the date when the number of tourists will drop to 49.8 thousand.
The linearization of a function works best when it is used to approximate a function, meaning behaviour and value, close to the point of tangency. A. True B. False
U.S. Population Over Age 16 The table gives theprojections of the population, in millions, of U.S.residents over age 16 for selected years 2015 to 2060.a. Graph the data, with y equal to the population inmillions and x equal to the number of years after2010.b. Find a linear function that models the data, with yequal to the population in millions and x equal to thenumber of years after 2010.c. Graph the model and the data on the same axesand comment on the fit of the model to the data.d. What does the model predict that the populationwill be in 2042?e. In what year does the model predict that the population will be 336.827 million?

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