Population Growth A major corporation is building a 4,325-acre complex of homes, offices, stores, schools, and churches in the rural com planners have estimated that Glen Cove's population (in thousands) t years from now will be given by P(t)= 20t² + 100t + 160 t² + 5t + 40 (a) Find the rate (in people/year) at which Glen Cove's population is changing with respect to time. P'(t) = (b) What will the population be after 10 years? (Round your answer to the nearest person.) Xx people At what rate (in people/year) will the population be increasing when t = 10? (Round your answer to the nearest integer.) people/year

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.6: Modeling With Exponential Functions
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Population Growth A major corporation is building a 4,325-acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the
planners have estimated that Glen Cove's population (in thousands) t years from now will be given by
20t² + 100t + 160
P(t):
t² + 5t + 40
(a) Find the rate (in people/year) at which Glen Cove's population is changing with respect to time.
P'(t) =
(b) What will the population be after 10 years? (Round your answer to the nearest person.)
X people
At what rate (in people/year) will the population be increasing when t = 10? (Round your answer to the nearest integer.)
Xpeople/year
=
Transcribed Image Text:Population Growth A major corporation is building a 4,325-acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Cove's population (in thousands) t years from now will be given by 20t² + 100t + 160 P(t): t² + 5t + 40 (a) Find the rate (in people/year) at which Glen Cove's population is changing with respect to time. P'(t) = (b) What will the population be after 10 years? (Round your answer to the nearest person.) X people At what rate (in people/year) will the population be increasing when t = 10? (Round your answer to the nearest integer.) Xpeople/year =
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