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(U2) Lesson 6 - Getting down to business

Last updated over 2 years ago
8 questions
Today's Learning Goal:
  • Model both linear and exponential functions with tables, graphs and equations.
  • Compare the end behavior of linear and exponential functions and make arguments about why exponential functions eventually exceed linear functions.
  • Make modeling decisions about whether a discrete or continuous model is more appropriate.
  • Interpret the point of intersection of two functions as the value that occurs when f(x) = g(x).
Reminders:
Discrete functions have distinct and separate values and are used for things that can be counted. (countable)
Continuous functions can have any value within a specific interval and values are connected. (measureable)
Domain of a function: The numbers that can be used as possible inputs
Today's Materials:
  1. Laptop
  2. Pencil
  3. Binder
Please complete the Jump Start (activator). This is independent it should be silent.
QUICK QUIZ 2 - 15 Minutes

Practice

Learning Focus:
  • Make modeling decisions about business plans.
  • Interpret mathematical models to make business decisions.
  • Determine which type of function grows faster and make arguments about why.
Which type of function increases faster—linear or exponential? Which model is best for a given situation, discrete or continuous?
How can mathematical models help to make business decisions?
Calcu-rama had a net income of $5 million in 2020, while a small competing company, Computafest, had a net income of $2 million.

The management of Calcu-rama develops a business plan for future growth that projects an increase in net income adding $0.5 million per year, while the management of Computafest develops a plan aimed at increasing its net income by 15% each year.
Required
1

Click the parts of the text that are most important mathematically.

Calcu-rama had a net income of $5 million in 2020, while a small competing company, Computafest, had a net income of $2 million.
The management of Calcu-rama develops a business plan for future growth that projects an increase in net income of $0.5 million per year, while the management of Computafest develops a plan aimed at increasing its net income by 15% each year.
Required
0

Create standard mathematical models (table, graph, and equations) for the projected net income over time for both companies.

Required
4

Compare the two companies:
Categorize the facts about each company based on the representations.

  • Graphs: Exponential Curve: Increases slowly in the first few years and then rises quickly.
  • Graphs: Straight line - Constant increase each year.
  • Tables: Increases at a constant rate of 0.5
  • Function Type: Exponential
  • Equations: 0.5 is the slope (Common difference),
    Y-intercept is 5 (Starting value)
  • Equations: The constant ratio of 1.15 is the base of the exponential.
    The initial value of 2 is multiplied.
  • Tables: Increases at 15% per year, making a constant ratio of 1.15.
  • Function Type: Linear

  • Calcu-rama

  • Computafest

Required
0

If both companies were able to meet their net income growth goals, which company would you choose to invest in? Why?

Required
1

Which company would make most money after 8 years?

Required
1

When would your projections suggest that the two companies have the same net income? How did you find this? Will they ever have the same net income again?

Required
1

Which company would make most money after 14 years?

Required
0

Why did we model as discrete or continuous? Explain.