Calculating Exponential Growth and Decay

The video tutorial explores how to calculate the growth of bacteria on a toothbrush using exponential functions. It explains exponential growth and decay, emphasizing the growth factor and decay factor. The tutorial provides a practical example of bacteria growing by 25% each hour, demonstrating how to apply the formula y = a(1 + r)^x to solve for the number of bacteria after a given time. The lesson concludes with a problem-solving exercise, reinforcing the concept of exponential growth and its rapid increase over time.

What is the term used to describe the rate at which a population grows or shrinks?

• Exponential constant

• Decay constant

• Population rate

• Growth factor

In the visual example, if a group of dots grows by 40%, what is the new growth factor?

• 1.4

• 0.6

• 0.4

• 2.4

Which equation represents exponential growth?

• y = a * (1 + r)^x

• y = a + r * x

• y = a * r^x

• y = a * x + r

What does a decay factor between 0 and 1 indicate?

• The population is growing

• The population is shrinking

• The population is stable

• The population is fluctuating

If a toothbrush starts with 5,000 bacteria and grows by 25% each hour, how many bacteria will be present after 8 hours?

• 10,000

• 20,000

• 15,000

• 29,800