Recursive and Explicit Formulas in Growth

This video tutorial covers linear growth, explaining both recursive and explicit forms. It uses examples like student population and streetlight installation to illustrate how to calculate future values using these methods. The tutorial highlights the advantages of explicit equations for long-term predictions and compares them to recursive formulas. It also connects these concepts to the slope-intercept form of linear equations.

What is the initial number of students at the college in the example provided?

• 3,500

• 125

• 4,000

• 5,600

In a recursive relationship, how is the next value in a sequence determined?

• By subtracting a constant from the previous value

• By adding a constant to the initial value

• By multiplying the previous value by a constant

• By relating it to the previous value or values

How many students are expected to attend the college after four years using the recursive formula?

• 5,600

• 3,625

• 3,750

• 4,000

What is the main advantage of using an explicit equation over a recursive formula?

• It only works for small time periods

• It is more complex to calculate

• It simplifies predictions for future values

• It requires knowledge of the previous term

Using the explicit equation, how many years will it take for the student population to reach 5,600?

• 16 years

• 18 years

• 15 years

• 17 years

What does the common difference 'D' represent in the context of linear growth?

• The final value

• The total population

• The rate of change per time period

• The initial value

In the slope-intercept form of a linear equation, what does the slope represent?

• The initial value

• The x-intercept

• The y-intercept

• The rate of change

How many streetlights will there be at the end of 42 weeks using the explicit formula?

• 128

• 254

• 126

• 42

What is the recursive formula for the streetlight example?

• P_sub_N = 128 + 3N

• P_sub_N = P_sub_N - 1 + 3

• P_sub_N = P_sub_0 + 128

• P_sub_N = P_sub_0 + 3N

What is the explicit formula for the streetlight example?

• P_sub_N = 128 + 3N

• P_sub_N = P_sub_N - 1 + 3

• P_sub_N = 3N + 128

• P_sub_N = 128N + 3