question archive In this module you have learned about exponential growth and decay
In this module you have learned about exponential growth and decay
Subject:MathPrice: Bought3
In this module you have learned about exponential growth and decay. These types of models can be used for situations in which the increase or decrease in a population becomes more rapid as time passes. On paper, any population can grow or decay exponentially forever, but in the world outside the mathematics classroom there are often restrictions that cause the growth or decay to slow as time passes. This type of growth or decay is referred to logistic.
Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially. The growth from 2009 through 2015 can be modeled using the function where t is the number of years since 2009 and is measured in millions of smartphones.
Find the values and . Show your work and explain what these numbers mean in context of this scenario.
Suppose that the actual number of smartphones (in millions) shipped from manufacturers to stores in 2016 was 1,584 and the actual number is 2017 was 1,651. Does the model accurately reflect this growth? Explain why the given model is returning values that are so much higher than the actual numbers.
Nikola thinks that the model that reflects the growth of smartphones shipped from manufacturers to stores around the world may be logistic rather than exponential. Do you agree with Nikola? Why or why not?
HINT: Consider the differences between exponential and logistic growth, and how these differences apply to this scenario.
Let the function reflect the growth of the number of smartphones shipped from manufacturers to stores around the world, where t is the number of years since 2009 and is measured in millions. Find the year when the number of smartphones shipped around the world is 1,728. Interpret your answer.
