Exponential Growth of Bacteria

The video tutorial explains exponential growth using a bacteria culture example. Starting with 200 bacteria, the population grows to 900 in three hours. The exponential growth model is introduced, and the growth rate is calculated using logarithms. The tutorial demonstrates how to predict the population after six hours and determine the time required for the population to reach 5,000. Key concepts include exponential functions, growth rate calculation, and population prediction.

What is the initial number of bacteria in the culture?

• 100

• 200

• 300

• 400

After how many hours does the bacteria population reach 900?

• 4 hours

• 3 hours

• 2 hours

• 1 hour

Which of the following represents the exponential growth model used in the video?

• P(t) = P0 / e^(kt)

• P(t) = P0 * kt

• P(t) = P0 * e^(kt)

• P(t) = P0 + kt

What is the value of the exponential growth rate (K) derived in the video?

• 0.501359

• 0.601359

• 0.401359

• 0.301359

What mathematical operation is used to isolate the exponential part of the equation?

• Division

• Multiplication

• Subtraction

• Addition

Which property of logarithms is applied to solve for the growth rate K?

• Change of Base Property

• Power Property

• Product Property

• Quotient Property

What is the base of the natural logarithm used in the calculations?

• 5

• 2

• e

• 10

How many bacteria are present after six hours according to the model?

• 4,050

• 6,050

• 5,050

• 3,050

What is the approximate time required for the bacteria population to reach 5,000?

• 6.42 hours

• 8.42 hours

• 5.42 hours

• 7.42 hours

What is the final step to find the time when the population reaches 5,000?

• Add K

• Divide by K

• Subtract K

• Multiply by K