Alg2_M5_5
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Arizona State University *
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Course
301
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
3
Uploaded by ChefMetal11704
Module 5, Exponential & Logistic Growth Assignment
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
𝐺𝐺
(
𝑡𝑡
) =
174 • 1.67
𝑡𝑡
where
t
is the number of years since 2009 and
𝐺𝐺
(
𝑡𝑡
)
is
measured in millions of smartphones.
Use this information and your knowledge of exponential and logistic
growth to explore the mathematical concepts in the questions below.
1. Create a graph of the function
𝐺𝐺
(
𝑡𝑡
)
and explain the meaning of the y-intercept in terms of the
number of smartphones being shipping to stores.
2. Explain a way you could calculate exactly when smartphone manufacturers were shipping 500
million smartphones to stores around the world.
3. Use your plan from question 2 to find when smartphone manufacturers were shipping 750
million smartphones to stores around the world. If you are solving algebraically, explain which
properties of logarithms you used and why.
4. Find the values
𝐺𝐺
(7)
and
𝐺𝐺
(8)
. Show your work and explain what these numbers mean in
context of this scenario.
5. 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
𝐺𝐺
(
𝑡𝑡
) =
174 • 1.67
𝑡𝑡
accurately reflect this growth? Explain why the given model is returning values
that are so much higher than the actual numbers.
6. 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.
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