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Question 9 ( :) The demand for nurses in the US between 2000 and 2015 is estimated to be: D(t) = 0.7t² + 0.265t + 2000 thousand where 0

Question 9 ( :) The demand for nurses in the US between 2000 and 2015 is estimated to be: D(t) = 0.7t² + 0.265t + 2000 thousand where 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Question 9 ( :) The demand for nurses in the US between 2000 and 2015 is estimated to be: D(t) = 0.7t2 + 0.265t + 2000 thousand where 0 <t< 15, and t = 0 corresponds to year 2000. The number of nurses in the US between 2000 and 2015 is estimated to be: S(t) = 0.14t2 + 0.326t + 1900 thousand where 0 <t< 15, and t = 0 corresponds to year 2000. a) Find D(8) and interpret. b) Find S(8) and interpret. c) Find S(8)/D(8) and interpret. d) Find D'(t). e) Find S'(t). f) Find and interpret D'(8). Make sure to state the correct units. g) Find and interpret S'(8). Make sure to state the correct units. h) Let q(t) = S(t)/D(t). Find and interpret q'(8). (You do not need to find q'(t) for general t) i) In marginal analysis, you would use q' (8) to estimate what quantity? Find the exact value of that quantity and compare with q'(8).
Transcribed Image Text:Question 9 ( :) The demand for nurses in the US between 2000 and 2015 is estimated to be: D(t) = 0.7t2 + 0.265t + 2000 thousand where 0 <t< 15, and t = 0 corresponds to year 2000. The number of nurses in the US between 2000 and 2015 is estimated to be: S(t) = 0.14t2 + 0.326t + 1900 thousand where 0 <t< 15, and t = 0 corresponds to year 2000. a) Find D(8) and interpret. b) Find S(8) and interpret. c) Find S(8)/D(8) and interpret. d) Find D'(t). e) Find S'(t). f) Find and interpret D'(8). Make sure to state the correct units. g) Find and interpret S'(8). Make sure to state the correct units. h) Let q(t) = S(t)/D(t). Find and interpret q'(8). (You do not need to find q'(t) for general t) i) In marginal analysis, you would use q' (8) to estimate what quantity? Find the exact value of that quantity and compare with q'(8).
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