Exploring Exponential Decay Functions

The video tutorial covers exponential functions, focusing on growth and decay. It begins with a review of exponential growth functions, highlighting their rapid increase when the base is greater than one. The tutorial then introduces exponential decay functions, where the base is less than one, and explains how they can also be represented with a negative exponent. The video includes plotting examples of decay functions and concludes with a word problem involving bacterial population decay, demonstrating how to calculate and graph the population over time.

What is the y-intercept of an exponential growth function with a positive base?

• Undefined

• 1

• The base itself

• 0

If the base of an exponential function is 10, how does the growth rate compare to a base of 2?

• Slower

• Faster

• Depends on the exponent

• The same

What is an example of an exponential decay function?

• y = x^3

• y = (1/3)^x

• y = 1/x

• y = 3^x

How can y = (1/3)^x be rewritten to show a negative exponent?

• (3/x)^-1

• 3^(1/x)

• x^(-3)

• 3^(-x)

What is the value of y when x = -1 for the function y = (1/3)^x?

• 3

• 27

• 1/3

• 9

What happens to the y-values as x increases in an exponential decay function?

• Decreases

• Increases

• Becomes negative

• Remains constant

By what factor does the antibiotic reduce the bacterial population each day?

• 1/2

• 1/5

• 1/3

• 1/4

What is the population of bacteria on day 1 after taking the antibiotic?

• 250,000

• 2 million

• 1 million

• 500,000

What is the general formula for the bacterial population on day n?

• (1/3)^n * 2 million

• 2^n * 2 million

• (1/2)^n * 2 million

• (1/4)^n * 2 million

How many bacteria are estimated to remain 10 days after the antibiotic treatment?

• 190

• 1900

• 19

• 1.9