Student Population Functions and Models

The video tutorial explains how to model student population changes in a charter school using linear and exponential functions. It covers the use of function notation to represent the number of students over time, distinguishing between constant amount changes (linear) and constant percentage changes (exponential). Examples are provided to illustrate both types of models, including scenarios of increasing and decreasing populations, as well as a constant population scenario.

What was the initial student population when the Charter School opened in 1980?

• 800

• 850

• 890

• 900

Which type of function is used to model a student population that changes by a constant amount each year?

• Exponential

• Linear

• Quadratic

• Logarithmic

What does the slope 'M' represent in a linear function modeling student population?

• Percentage change

• Initial population

• Change in population per year

• Total population

How is the growth factor 'b' calculated in an exponential function for increasing student population?

• 1 minus r

• 1 plus r

• r divided by 2

• r squared

In a linear function, if the student population decreases by 40 students per year, what is the slope 'M'?

• 0

• -40

• 40

• 890

What is the decay factor 'b' if the student population decreases by 7.1% per year?

• 1.929

• 1.071

• 0.929

• 0.071

If the student population increases by 17% per year, what is the growth factor 'b'?

• 1.17

• 0.83

• 1.07

• 1.27

What is the base 'b' in an exponential function if the student population grows by 8.6% annually?

• 0.914

• 1.86

• 1.086

• 0.086

What type of function models a student population that remains constant over time?

• Linear

• Exponential

• Quadratic

• Constant

If the student population does not change, what is the function n(T) equal to?

• T

• 890

• T + 890

• 0