2. The population of a small town has been growing and is shown in the table belowt, the years since 1980102030P(t), the population1500 | 2329 | 36185618(a) What is the average number of people added to the town per year between 1980 and 1990?(b) Assuming that the population continues to grow exponentially, write a function equation for P(t).Justify your solution algebraically.(c) Use regression in Desmos to check your answer to Part (b) by entering the table and typing theexpression y1 ~ a · b®1.

Answered: Image /qna-images/answer/57df44ce-c615-4c66-a411-900d746bd05c.jpg

Answered: 2. The population of a small town has…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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1. The average per-person annual consumption of sports drinks in the U.S. is shown in the table for various years. Let C be the average per-person annual consumption (in gallons per person) of sports drinks at t years since 2000. a) Use your GC to find the regression equation to model the data. b) Rewrite your equation using function notation, C(t). Year 2002 2003 2004 2005 2006 d) What is the slope? What does it mean in this application? Annual Consumption (gallons per person) 2.7 3.0 3.4 4.1 4.5 c) Use your equation to predict the average annual per-person sports drink consumption in 2012.
The figure shown to the right contains a scatter plot of 10 data points for trees, where the diameter of a tree at breast height (Dbh) is given in inches and the height is given in feet. The regression model is shown below, where x is the Dbh in inches and y is the height in feet. y = 0.91x +4.39 (A) Interpret the slope of the model. O A. The rate of change of height with respect to Dbh is 4.39 in/ft. O B. The rate of change of height with respect to Dbh is 0.91 ft/in. O C. The rate of change of height with respect to Dbh is 4.39 ft/in. O D. The rate of change of height with respect to Dbh is 0.91 in/ft. Height (ft) 40- 0 16 Dbh (in) 25
The annual expenditure for cell phones varies by the age of an individual. The average annual expenditure E(a) (in $) for individuals of age a (in years) is given below:a: 20, 30, 40, 50, 60, 70E(a): 502, 658, 649, 627, 476, 2131. Use quadratic regression to find the model that best represents the data.2. At what age is the yearly expenditure for cell phones the greatest? Round the answer to the nearest year. YOU MUST SHOW THE WORK FOR THIS PART!
The table below shows the value, V, of an investment (in dollars) n years after 1992. 1 3 7 4120 4283 4919 12 14 5874 6050 n V(n) 6663 Use your calculator to determine the exponential regression equation that models the set of data above. Round the "a" value to the nearest whole number, and round the "b" value to three decimals. Use the indicated variables and proper function notation. V(n) Based on the your regression model, what is the percent increase per year? The value of this investment is increasing at a rate of % per year. Based the your regression model, what is value of this investment in the year 1992? Round your answer to the nearest dollar. The value of this investment is $ in the year 1992. Based on the your regression model, what is value of this investment in the year 2002? Round your answer to the nearest dollar. The value of this investment is S in the year 2002.
(d) If the life expectancy is increased by 3.5 years in a certain country, how much will the happiness index change? Round to two decimal places. (e) Use the regression line to predict the happiness index of a country with a life expectancy of 84 years. Round to two decimal places.
One of the two tables below shows data that are better approximated with a linear function, and the other shows data that are better approximated with an exponential function. Make plots to identify which is which, and then use the appropriate regression to find models for both. Round all numbers to three decimal places. t f(t) f(t) 1 3.62 1 3.62 The Linear Equation: The Exponential Equation: 2 23.01 (7 2 5.63 ( 3 44.26 8.83 4 62.17 13.62 51 83.25 5 21.22
Regression (1) in Table 1 estimates the effect of additional educationby regressing ln (W age) on Exp, Exp2, W ks, Ed and all the dummyvariables listed above. Does the estimated regression suggest that additional years of schooling increases the wage?

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