Exponential Growth and Recursive Formulas

The video tutorial explains how a population grows according to an exponential growth model. It starts with an initial population of 16 and a growth rate of 35%. The tutorial covers both recursive and explicit formulas for calculating future population sizes. The recursive formula uses the previous population value, while the explicit formula allows direct calculation for any time period. The video concludes with instructions on rounding results to one decimal place.

What is the initial population in the exponential growth model discussed?

• 10

• 16

• 35

• 20

What is the growth rate used in the model?

• 0.55

• 0.45

• 0.35

• 0.25

In the recursive formula, what is the value of 1 + R?

• 1.25

• 1.35

• 1.40

• 1.30

What is the population value P1 calculated using the recursive formula?

• 21.6

• 18.5

• 20.5

• 19.6

How is the next population value determined in the recursive formula?

• By subtracting a constant value

• By adding a constant value

• By using the previous population value

• By multiplying by a fixed number

What is the explicit formula for Pn in exponential growth?

• Pn = P0 - R^n

• Pn = P0 * (1 + R)^n

• Pn = P0 / (1 + R)^n

• Pn = P0 + R^n

What is the value of P0 in the explicit formula?

• 12

• 16

• 10

• 14

Using the explicit formula, what is the approximate population at n = 11?

• 400.3

• 414.3

• 424.3

• 434.3

What should you do if the directions say to round to at least one decimal place?

• Round to the nearest whole number

• Round to the nearest tenth

• Round to the nearest hundredth

• Do not round