Population Growth and Recursive Formulas

The video tutorial explains how a population grows using a recursive rule, identifying it as linear growth with a common difference. It demonstrates calculating the first two terms, P sub 1 and P sub 2, using the recursive formula. The tutorial then transitions to deriving an explicit equation from the recursive one, highlighting its equivalence to a linear equation. Finally, it applies the explicit equation to find the 100th term, P sub 100, illustrating the practical use of the formula.

What is the initial population value given in the recursive rule?

• 10

• 20

• 30

• 40

What is the common difference in the recursive formula for population growth?

• 100

• 120

• 110

• 130

How do you calculate P1 using the recursive formula?

• P0 + 100

• P0 + 110

• P0 + 120

• P0 + 130

What is the value of P1?

• 120

• 130

• 140

• 150

How do you calculate P2 using the recursive formula?

• P1 + 110

• P1 + 100

• P1 + 120

• P1 + 130

What is the value of P2?

• 270

• 260

• 250

• 240

What is the explicit equation for the population growth?

• P(n) = 20 + 100n

• P(n) = 20 + 110n

• P(n) = 20 + 130n

• P(n) = 20 + 120n

In the explicit equation, what does the common difference represent?

• The final population

• The initial population

• The rate of growth

• The time period

How do you calculate P100 using the explicit equation?

• 20 + 100 * 100

• 20 + 110 * 100

• 20 + 130 * 100

• 20 + 120 * 100

What is the value of P100?

• 11,000

• 12,000

• 12,200

• 12,020