Aurora, Nevada, was a mining boomtown in the 1860s and 1870s. Its population can be modeled as S-7.91t + 120.96t2 + 193.92t – 123.21 ( 45,544(0.8474) when 0.7 < t< 13 p(t) = %3D when 13 < t< 55 where p is measured in people and rate-of-change function -23.73t2 + 241.92t + 193.92 when 0.7

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.5: Linear Functions And Models
Problem 6E
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Aurora, Nevada, was a mining boomtown in the 1860s and 1870s. Its population can be modeled as
S-7.91t + 120.96t2 + 193.92t – 123.21
( 45,544(0.8474)
when 0.7 < t< 13
p(t) =
%3D
when 13 < t< 55
where p is measured in people and rate-of-change function
-23.73t2 + 241.92t + 193.92
when 0.7 <t< 13
p'(t) =
-7541.28(0.84745)
when 13 < t< 55
where p' is measured in people per year. In both functions, t is the number of years since 1860.t
(a) What was the average population of Aurora between 1863 and 1873? (Round your answer to the nearest integer.)
реople
(b) What what the average rate of change of the population of Aurora between 1863 and 1873? (Round your answer to two decimal places.)
people per year
Transcribed Image Text:Aurora, Nevada, was a mining boomtown in the 1860s and 1870s. Its population can be modeled as S-7.91t + 120.96t2 + 193.92t – 123.21 ( 45,544(0.8474) when 0.7 < t< 13 p(t) = %3D when 13 < t< 55 where p is measured in people and rate-of-change function -23.73t2 + 241.92t + 193.92 when 0.7 <t< 13 p'(t) = -7541.28(0.84745) when 13 < t< 55 where p' is measured in people per year. In both functions, t is the number of years since 1860.t (a) What was the average population of Aurora between 1863 and 1873? (Round your answer to the nearest integer.) реople (b) What what the average rate of change of the population of Aurora between 1863 and 1873? (Round your answer to two decimal places.) people per year
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