Population Decay and Growth Concepts

The video tutorial explains a standard proportionality setup with a negative constant k, indicating a decreasing population. It derives the growth rate, which is negative, and discusses its implications. The tutorial estimates the population after five years, considering rounding issues. It then explores a modified situation using a differential equation, analyzing the behavior as time approaches infinity.

What does a negative value of k imply about the population?

• The population is decreasing.

• The population is stable.

• The population is fluctuating.

• The population is increasing.

In the standard exponential decay formula, what does the term 'a' represent?

• The decay constant

• The growth rate

• The time period

• The initial population

What is the significance of the decay constant k in population models?

• It shows the time taken for population to double

• It defines the speed of population decline

• It indicates the maximum population

• It determines the initial population

In the context of the video, what does the term 'half-life' refer to?

• The time taken for the population to stabilize

• The time taken for the population to reach zero

• The time taken for the population to halve

• The time taken for the population to double

How is the decay constant k expressed as a percentage?

• By dividing by 100

• By subtracting 100

• By multiplying by 100

• By adding 100

What is the effect of a larger negative value of k on the population decline?

• The population declines more slowly

• The population remains constant

• The population increases

• The population declines more quickly

Why is it important to specify whether you round up or down when dealing with population numbers?

• Because it alters the decay constant

• Because populations cannot be fractional

• Because it changes the initial population

• Because it affects the growth rate

How do you calculate the population after a certain time using the decay constant?

• By adding the decay constant to the initial population

• By dividing the initial population by the decay constant

• By multiplying the initial population by e raised to the power of the decay constant times time

• By subtracting the decay constant from the initial population

What happens to the population as time approaches infinity in the modified situation?

• It becomes infinite

• It stabilizes at a certain value

• It continues to decrease indefinitely

• It fluctuates randomly

In the modified situation, what is the initial value of c when t equals zero?

• 250

• 50

• 200

• 100