Exponential Functions and Bacterial Growth

The video tutorial explains how to model the growth of a bacteria culture using an exponential function. Starting with an initial count of 1,200 bacteria that doubles every half hour, the tutorial demonstrates how to calculate the population size after 70 minutes and 4 hours. The exponential function is formulated with a base of 2, reflecting the doubling time, and the exponent is determined by dividing time in minutes by 30. Calculations show approximately 6,048 bacteria after 70 minutes and 307,200 bacteria after 4 hours.

What is the initial number of bacteria in the culture?

• 1,500

• 2,000

• 1,200

• 1,000

How often does the bacteria culture double in size?

• Every 30 minutes

• Every hour

• Every 45 minutes

• Every 15 minutes

In the exponential function P(t) = A * B^t, what does 'A' represent?

• Growth rate

• Initial amount

• Doubling time

• Time

What base is used in the exponential function for this problem?

• e

• 10

• 1.5

• 2

What is the exponent in the function P(t) = 1200 * 2^(t/30) when t is 30?

• 1

• 0

• 3

• 2

How many bacteria are there after 70 minutes?

• 7,200

• 5,000

• 8,000

• 6,048

What is the value of t in minutes for 4 hours?

• 120

• 180

• 240

• 300

How many bacteria are there after 4 hours?

• 400,000

• 100,000

• 200,000

• 307,200

What is the simplified exponent for the population after 4 hours?

• 8

• 9

• 7

• 6

Which of the following best describes the growth of the bacteria culture?

• Exponential growth

• Logarithmic growth

• Quadratic growth

• Linear growth