Exponential Growth Concepts and Applications

This video tutorial covers exponential growth, explaining both recursive and explicit formulas. It uses an example of an ant colony to demonstrate how to calculate growth rate and multiplier. The tutorial shows how to use these formulas to determine population after a set period and graphically find when the population reaches a specific number.

What is the primary focus of this lesson on exponential growth?

• Studying logarithmic functions

• Learning about quadratic equations

• Exploring recursive and explicit forms

• Understanding linear growth

In the recursive formula for exponential growth, what is required to find the next term?

• The time period

• The previous term

• The growth rate

• The initial population

What is the growth multiplier in exponential growth?

• The time period

• The initial size

• The growth rate as a percentage

• The sum of one and the growth rate

How is the growth rate expressed in the formulas?

• As a fraction

• As a percentage

• As a whole number

• As a decimal

What is the growth rate of the ant colony if P0 = 80 and P1 = 92?

• 25%

• 20%

• 15%

• 10%

What is the recursive formula for the ant colony's growth?

• P_n = 1.10 x P_n-1

• P_n = 92 x 1.15^n

• P_n = 80 x 1.15^n

• P_n = 1.15 x P_n-1

Using the explicit formula, what is the population of ants after 30 days?

• 7,200

• 6,000

• 5,297

• 4,500

What method is used to graphically determine when the population reaches 990?

• Substitution method

• Trial and error method

• Elimination method

• Intersection method

What is the approximate number of days for the ant population to reach 990?

• 15 days

• 18 days

• 20 days

• 25 days

Which tool is used to find the point of intersection in the graphical method?

• Protractor

• Ruler

• Calculator

• Compass