Population Growth and Linear Functions

The video tutorial explains a linear growth model problem where the number of members grows over time. It starts with an initial number of members and provides a method to find the common difference using both an explicit formula and a graphical approach. The tutorial also demonstrates how to calculate the number of weeks required for the membership to reach a specific number using the derived formula.

What is the initial number of members in the problem?

• 15

• 12

• 20

• 10

Which formula is used to calculate the number of members after n weeks?

• P sub n = P sub 0 + D * n

• P sub n = P sub 0 + D

• P sub n = P sub 0 * n

• P sub n = D * n

How is the common difference D calculated using the explicit formula?

• By dividing the initial number by 7

• By subtracting 12 from 75 and dividing by 7

• By adding 12 to 75

• By multiplying 75 by 7

What is the value of the common difference D?

• 9

• 8

• 7

• 10

How can the common difference also be found using the change in population?

• By dividing the change in population by the change in weeks

• By adding the change in weeks

• By multiplying the change in weeks

• By subtracting the change in weeks

What does the slope of the line represent in this problem?

• The final number of members

• The total number of weeks

• The common difference

• The initial number of members

Which ordered pair represents the initial condition on the graph?

• (7, 12)

• (7, 75)

• (0, 75)

• (0, 12)

What is the slope of the line passing through the points (0, 12) and (7, 75)?

• 7

• 8

• 9

• 10

How many weeks will it take for the number of members to reach 228?

• 26 weeks

• 24 weeks

• 22 weeks

• 20 weeks

What is the final step in solving for the number of weeks to reach 228 members?

• Add 12 to 216

• Divide 216 by 9

• Subtract 12 from 228

• Multiply 9 by 24