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Let p(t) represent the population of a major city t years after 1950, as shown in the table and figure. Answer parts (a) through (c) below. Year 1950 1960 1970 1980 1990 2000 0 10 20 30 40 50 59,000 114,153 220,862 427,322 826,779 1,599,646 t p(t) a. Compute the average rate of growth of the city population from 1970 to 1980. The average rate of growth is people/year. (Simplify your answer. Type an integer a decimal. Round to the nearest tenth as needed.) OB. The formula Population (thousands) b. Explain why the average rate of growth calculated in part (a) is a good estimate of the instantaneous rate of growth of the city in 1975. Choose the correct answer below. p(30)-p(20) 30-20 2000 1600 1200 OA. The average rate of growth from 1970 to 1980 equals the slope of the secant line through points (20,p(20)) and (30,p(30)). 800] 400 F---- 0000 0 10 20 30 40 50 Years after 1950 gives the instantaneous rate of population change in 1975. OC. The slope of the tangent line at t = 25 is approximately equal to the slope of the secant line through points (20,p(20)) and (30,p(30)).

Let p(t) represent the population of a major city t years after 1950, as shown in the table and figure. Answer parts (a) through (c) below. Year 1950 1960 1970 1980 1990 2000 0 10 20 30 40 50 59,000 114,153 220,862 427,322 826,779 1,599,646 t p(t) a. Compute the average rate of growth of the city population from 1970 to 1980. The average rate of growth is people/year. (Simplify your answer. Type an integer a decimal. Round to the nearest tenth as needed.) OB. The formula Population (thousands) b. Explain why the average rate of growth calculated in part (a) is a good estimate of the instantaneous rate of growth of the city in 1975. Choose the correct answer below. p(30)-p(20) 30-20 2000 1600 1200 OA. The average rate of growth from 1970 to 1980 equals the slope of the secant line through points (20,p(20)) and (30,p(30)). 800] 400 F---- 0000 0 10 20 30 40 50 Years after 1950 gives the instantaneous rate of population change in 1975. OC. The slope of the tangent line at t = 25 is approximately equal to the slope of the secant line through points (20,p(20)) and (30,p(30)).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 35E
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c. Compute the average rate of growth of the city from 1990 to 2000. The average rate of growth is people/year. (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.) Is this average rate of growth an overestimate or underestimate of the instantaneous rate of growth of the city in 2000? Underestimate O Overestimate Approximate the growth rate of the city's population in 2000. The instantaneous rate of growth is about people/year. (Simplify your answer. Round to the nearest ten thousand as needed.)
Transcribed Image Text:c. Compute the average rate of growth of the city from 1990 to 2000. The average rate of growth is people/year. (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.) Is this average rate of growth an overestimate or underestimate of the instantaneous rate of growth of the city in 2000? Underestimate O Overestimate Approximate the growth rate of the city's population in 2000. The instantaneous rate of growth is about people/year. (Simplify your answer. Round to the nearest ten thousand as needed.)
Let p(t) represent the population of a major city t years after 1950, as shown in the table and figure. Answer parts (a) through (c) below. Year 1950 1960 1970 1980 1990 2000 t 0 10 20 30 40 50 p(t) 59,000 114,153 220,862 427,322 826,779 1,599,646 a. Compute the average rate of growth of the city population from 1970 to 1980. The average rate of growth is people/year. (Simplify your answer. Type an integer a decimal. Round to the nearest tenth as needed.) OB. Population (thousands) b. Explain why the average rate of growth calculated in part (a) is a good estimate of the instantaneous rate of growth of the city in 1975. Choose the correct answer below. p(30)-p(20) 30-20 The formula 2000 1600 1200 OA. The average rate of growth from 1970 to 1980 equals the slope of the secant line through points (20,p(20)) and (30,p(30)). 800] 400 F‒‒‒‒ 0000 0 10 20 30 40 50 Years after 1950 gives the instantaneous rate of population change in 1975. OC. The slope of the tangent line at t = 25 is approximately equal to the slope of the secant line through points (20,p(20)) and (30,p(30)).
Transcribed Image Text:Let p(t) represent the population of a major city t years after 1950, as shown in the table and figure. Answer parts (a) through (c) below. Year 1950 1960 1970 1980 1990 2000 t 0 10 20 30 40 50 p(t) 59,000 114,153 220,862 427,322 826,779 1,599,646 a. Compute the average rate of growth of the city population from 1970 to 1980. The average rate of growth is people/year. (Simplify your answer. Type an integer a decimal. Round to the nearest tenth as needed.) OB. Population (thousands) b. Explain why the average rate of growth calculated in part (a) is a good estimate of the instantaneous rate of growth of the city in 1975. Choose the correct answer below. p(30)-p(20) 30-20 The formula 2000 1600 1200 OA. The average rate of growth from 1970 to 1980 equals the slope of the secant line through points (20,p(20)) and (30,p(30)). 800] 400 F‒‒‒‒ 0000 0 10 20 30 40 50 Years after 1950 gives the instantaneous rate of population change in 1975. OC. The slope of the tangent line at t = 25 is approximately equal to the slope of the secant line through points (20,p(20)) and (30,p(30)).
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