Math Problem Statement

In 2009, 2012, and 2015, the number of smartphones sold in the world was 1674, 6351, and 14188, respectively. Let t represent time in years since 2009, and let S(t) represent the number of smartphones sold in millions. Determine M, A, and k in a logistic model, S(t) = M / (1 + A e^(-kt)), that fits the given data points.

Solution

The image provides a question with similar data points as the previous one, involving smartphone sales for the years 2009, 2012, and 2015. The task is to determine the values of MM, AA, and kk using a logistic model:

S(t)=M1+AektS(t) = \frac{M}{1 + A e^{-kt}}

with the following data points:

  • 2009: S(0)=1674S(0) = 1674 million
  • 2012: S(3)=6351S(3) = 6351 million
  • 2015: S(6)=14188S(6) = 14188 million

The prompt asks for the values of MM and AA to be rounded to three decimal places and MM to one decimal place.

Based on your previous input, where M3756.4M \approx 3756.4, A11.1A \approx 11.1, and ( k \approx 0.

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Math Problem Analysis

Mathematical Concepts

Logistic growth model
Exponential functions

Formulas

S(t) = M / (1 + A e^(-kt))

Theorems

Logistic growth

Suitable Grade Level

University level or advanced high school (Grades 11-12)