43. City urbanization City planners model the size of their city using 1 t<50, where A t2t20, for 0 50 the function A(t) is measured in square miles and t is the number of years after 2010. a. Compute A'(t). What units are associated with this derivative and what does the derivative measure? b. How fast will the city be growing when it reaches a size of 38 mi2? c. Suppose the population density of the city remains constant from year to year at 1000 people/mi2. Determine the growth rate of the population in 2030.

Question
43. City urbanization City planners model the size of their city using
1
t<50, where A
t2t20, for 0
50
the function A(t)
is measured in square miles and t is the number of years after 2010.
a. Compute A'(t). What units are associated with this derivative
and what does the derivative measure?
b. How fast will the city be growing when it reaches a size of
38 mi2?
c. Suppose the population density of the city remains constant
from year to year at 1000 people/mi2. Determine the growth
rate of the population in 2030.

Image Transcription

43. City urbanization City planners model the size of their city using 1 t<50, where A t2t20, for 0 50 the function A(t) is measured in square miles and t is the number of years after 2010. a. Compute A'(t). What units are associated with this derivative and what does the derivative measure? b. How fast will the city be growing when it reaches a size of 38 mi2? c. Suppose the population density of the city remains constant from year to year at 1000 people/mi2. Determine the growth rate of the population in 2030.

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