Exponential Growth and Decay Concepts

Mr. Bean's lesson covers percent increase and decrease, modeling these changes in equations, and understanding half-life and doubling time. The lesson also explores equivalent forms of exponential functions, providing students with a comprehensive understanding of these mathematical concepts.

What is the main focus of today's lesson in AP Pre-Calculus?

• Graphing linear functions

• Solving quadratic equations

• Calculating derivatives

• Understanding percent increase and decrease

If a quantity increases by 97%, what is the new base of the exponent?

• 0.97

• 1.97

• 1.07

• 2.97

How do you express a 5% decrease in terms of the base of an exponent?

• 1.05

• 0.5

• 0.95

• 1.5

What is the percent increase if the base of the exponent is 1.2?

• 30%

• 20%

• 10%

• 40%

What is the percent decrease if the base of the exponent is 0.7?

• 20%

• 10%

• 40%

• 30%

In a modeling scenario, if a home's value increases by 1.5% per year, what is the base of the exponent?

• 1.015

• 1.15

• 1.5

• 0.015

What is the base of the exponent for a 28.1% decrease?

• 0.719

• 1.281

• 1.719

• 0.281

What is the concept of half-life used to describe?

• The time it takes for a quantity to reduce by half

• The time it takes for a quantity to triple

• The time it takes for a quantity to remain constant

• The time it takes for a quantity to double

In the context of half-life, what does the variable 'H' represent?

• The initial amount

• The time variable

• The doubling time

• The half-life duration

What does the doubling time formula help determine?

• The time it takes for a quantity to double

• The initial amount of a quantity

• The rate of decrease of a quantity

• The time it takes for a quantity to halve