Exponential Growth and Bacteria Modeling

The video tutorial explains the exponential growth of bacteria in a culture using the function N(t) = 500 x e^(0.15t). It covers the components of exponential growth functions, including time (t), growth rate (k), initial population (P0), and population after time (P(t)). The tutorial demonstrates how to calculate the growth rate as a percentage, determine the initial population, and find the population after a specific time, such as 12 hours. The video concludes with a practical example using a calculator to verify the calculations.

What is the function used to model the number of bacteria in a culture?

• N(t) = 200 * e^(0.2t)

• N(t) = 300 * e^(0.05t)

• N(t) = 500 * e^(0.15t)

• N(t) = 1000 * e^(0.1t)

In the general exponential growth function P(t) = P0 * e^(kt), what does 'k' represent?

• Initial population

• Final population

• Time in hours

• Exponential growth rate as a decimal

How do you convert the growth rate 'k' to a percentage?

• Subtract 100

• Add 100

• Divide by 100

• Multiply by 100

What is the growth rate as a percentage for the given function N(t) = 500 * e^(0.15t)?

• 10%

• 25%

• 15%

• 20%

What is the initial population of bacteria according to the function N(t) = 500 * e^(0.15t)?

• 100 bacteria

• 200 bacteria

• 500 bacteria

• 1000 bacteria

How can you verify the initial population using the function N(t) = 500 * e^(0.15t)?

• Calculate N(1)

• Calculate N(3)

• Calculate N(0)

• Calculate N(2)

What is the value of e^0?

• Infinity

• 0

• 1

• e

How many bacteria are present after 12 hours according to the function N(t) = 500 * e^(0.15t)?

• 3,025 bacteria

• 4,000 bacteria

• 2,500 bacteria

• 1,500 bacteria

Which mathematical operation is used to evaluate the function N(t) = 500 * e^(0.15t) for t = 12?

• Exponentiation

• Multiplication

• Addition

• Subtraction

What tool is suggested to evaluate the exponential function for t = 12?

• Slide rule

• Graph paper

• Abacus

• Calculator