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 wasthousands.(Round to the nearest integer as needed.)

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Answered: The U.S. population can be modeled by…

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 number (in thousands) of women in the work force as function of the year is shown in the figure below. Calculate and interpret the following in your case study report. Evaluate f(1983) and f(2011) using the graph. Solve f(year) = 50,000,000 using the graph. Solve f(year) = 43,000,000 using the graph. Estimate f(2014) - f(1994) using the graph. What are the natural domain and range of this function?
9. A car loses value each year. The value of the car t years from today can be modeled using the 1 function (t) = 15,000(0.85). If Elizabeth wants to sell her car in 2- years, what will the car's %3D 3 value be when she sells it?
Actinium is a radioactive soft metal that glows light blue in the dark. The isotope actinium-228 has a half-life of about 21.77 years. Suppose a laboratory worked with a 1.65 milligram sample of actinium-228. What function could be used to represent the amount, AA, in milligrams of the actinium-228 sample after tt years?
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
The cost of a new car is $32,000. It depreciates at a rate of 15% per year. This means that it loses 15% of the value each year. a) The function that models the value of the car (in thousands) at the end of each year is ___________ . (Enter your equation without spaces, with parentheses around the b value, and using a caret for the exponent, such as y=3(1.25)^t . b) The value of the car after 4 years will be ______.
.034x The assets (in billions of dollars) for a financial firm can be approximated by the function A(x) = 319e where x = 7 corresponds to the year 2007. Find the assets in each of the following years. (a) 2011 (b) 2015 (c) 2017 (a) Which of the following describes how to find the assets in 2011 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) .034x O A. To find the assets in 2011, find the intersection point of the graphs y = 319e and y = 2011 are represented by the y-coordinate. O B. To find the assets in 2011, substitute for x and evaluate to find A(x). The assets in
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.
6. You have a device that monitors the sound level of a conversation located 1 meter away. The results are shown in the graph. a. Describe the relationship of the sound level as a function of time. Sound Level (dB) ty (1) (2) (3) X
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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.)
Throughout much of the 20th century, the yearly consumption of electricity in the US increased exponentially at a continuous rate of 7% per year. Assume this trend continues and that the electrical energy consumed in 1900 was 1.5 million megawatt-hours. (a) Write an expression for yearly electricity consumption, E, as a function of time, t, in years since 1900. million megawatt-hours (b) Find the average yearly electrical consumption throughout the 20th century. NOTE: Round your answer to the nearest integer. E(t) = million megawatt-hours (c) During what year was electrical consumption closest to the average for the century? NOTE: Round your answer to the nearest integer. During Average Yearly Consumption =
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