In 2009, 2012, and 2015, the number (in millions) of smart phones sold in the world was 172.4, 680.1, and 1423.9, respectively. (a) Let t represent time in years since 2009, and let S represent the number of smart phones sold in millions. Determine M, A, and k for a logistic model, S(t) = M 1+Ae¬kt , that fits the given data points. (Use decimal notation. Give your answers to three decimal places. Use a CAS for calculations.) M = A = k = (b) What is the long-term expected maximum number of smart phones sold annually? That is, what is lim S(t)? (Use decimal notation. Give your answer to three decimal places.) lim S(t) = million (c) In what year does the model predict that smart-phone sales will reach 85% of the expected maximum?
In 2009, 2012, and 2015, the number (in millions) of smart phones sold in the world was 172.4, 680.1, and 1423.9, respectively. (a) Let t represent time in years since 2009, and let S represent the number of smart phones sold in millions. Determine M, A, and k for a logistic model, S(t) = M 1+Ae¬kt , that fits the given data points. (Use decimal notation. Give your answers to three decimal places. Use a CAS for calculations.) M = A = k = (b) What is the long-term expected maximum number of smart phones sold annually? That is, what is lim S(t)? (Use decimal notation. Give your answer to three decimal places.) lim S(t) = million (c) In what year does the model predict that smart-phone sales will reach 85% of the expected maximum?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:In 2009, 2012, and 2015, the number (in millions) of smart phones sold in the world was 172.4, 680.1, and 1423.9, respectively.
(a) Let t represent time in years since 2009, and let S represent the number of smart phones sold in millions. Determine M, A,
and k for a logistic model, S(t) = -k that fits the given data points.
1+Ae-kt
(Use decimal notation. Give your answers to three decimal places. Use a CAS for calculations.)
M =
A =
k =
(b) What is the long-term expected maximum number of smart phones sold annually? That is, what is lim S(t)?
t00
(Use decimal notation. Give your answer to three decimal places.)
lim S(t) =
million
(c) In what year does the model predict that smart-phone sales will reach 85% of the expected maximum?
(Use decimal notation. Give your answer to two decimal places.)
t =
year(s) after 2009
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