Exponential Growth Model Concepts

The video tutorial explains how a population grows according to an exponential growth model. It covers finding the recursive and explicit formulas and calculating the growth factor and rate. The tutorial demonstrates how to use these formulas to find the population at a specific time, P of 5, using the explicit formula. The growth factor is calculated as 1.4, leading to a growth rate of 40%. The recursive formula is P_n = 1.4 * P_(n-1), and the explicit formula is P_n = 70 * 1.4^n. The video concludes with calculating P_5, which is approximately 376.5.

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

• 50

• 70

• 98

• 100

What is the growth factor in the exponential growth model?

• 1.3

• 1.5

• 1.2

• 1.4

How is the growth rate calculated from the growth factor?

• Subtract 1 from the growth factor

• Add 1 to the growth factor

• Divide the growth factor by 100

• Multiply the growth factor by 100

What is the growth rate percentage in the exponential growth model?

• 35%

• 40%

• 30%

• 45%

What is the recursive formula for the population growth?

• P_n = 1.5 * P_n-1

• P_n = 1.4 * P_n-1

• P_n = 1.3 * P_n-1

• P_n = 1.2 * P_n-1

What is the base value used in the explicit formula for the population growth?

• 80

• 50

• 60

• 70

In the explicit formula, what is the exponent applied to the growth factor?

• n

• n-1

• n+1

• 2n

Why is the explicit formula preferred over the recursive formula for finding P_5?

• It uses a different growth factor

• It is more accurate

• It requires fewer calculations

• It is easier to understand

What is the approximate value of P_5 after rounding?

• 377.5

• 376.5

• 375.5

• 378.5

What is the significance of the number 7 in the rounding process?

• It indicates rounding up

• It is multiplied by 10

• It indicates rounding down

• It is ignored