Exploring Exponential Growth and Decay

The video tutorial extends knowledge of exponential functions, focusing on what makes them grow or shrink. It explains the formula y = a * b^x, where 'b' is derived from increasing or decreasing a whole value by a percentage. The video provides examples of exponential growth and decay, using a painting's value and a town's population, respectively. It also covers how to identify whether a scenario represents growth or decay by analyzing the 'b' value in the formula.

What does the 'b' in the exponential function formula represent?

• The final value after x years

• Growth or decay rate as a percentage

• The total value

• The initial value

How do you convert a percentage to a decimal in the context of exponential functions?

• Move the decimal two places to the left

• Divide by 100

• Move the decimal two places to the right

• Multiply by 100

What does the 'r' in the exponential function formula represent?

• The final value after x years

• The initial value

• The total value

• Growth or decay rate as a percentage

What is the value of a painting after 25 years if it appreciates at 9% annually, starting from $1400?

• $15,000.00

• $14,200.00

• $12,072.31

• $10,500.00

In the context of exponential growth, what does 'f of t' represent?

• The final value after t years

• The percentage increase

• The decay rate

• The initial value

What does an exponential decay formula calculate?

• Increase in value over time

• Decrease in value over time

• Initial value

• Percentage increase

How is the population of a town in 2008 calculated if it decays at 1% annually from 1300 people in 2000?

• 1,999 people

• 1,200 people

• 1,300 people

• 1,100 people

What indicates exponential growth in a given function?

• The exponent is negative

• The base 'b' is less than one

• The base 'b' is equal to one

• The base 'b' is greater than one

What was the initial population of bees if the given exponential function represents their growth?

• 3,215 bees

• 4,000 bees

• 3,500 bees

• 2,000 bees

How do you determine if an exponential function represents growth or decay?

• By checking the exponent's value

• By checking if the base 'b' is greater or less than one

• By checking if the rate is positive or negative

• By checking if the initial value is greater than the final value