Mouse Population Dynamics and Functions

The video tutorial explains how the mouse population in an area during a drought can be modeled using a linear function. It covers the significance of the slope, which is negative two-thirds, indicating a decrease in population over time. The slope shows that for every three months, the population decreases by 2000 mice. The y-intercept, or initial value, is 5, representing the starting population of 5000 mice when no time has passed.

What does the variable 'x' represent in the function describing the mouse population?

• The initial population

• The rate of population change

• The time in months

• The number of mice

In the context of the mouse population function, what does the slope represent?

• The maximum population

• The change in population over time

• The time in months

• The initial population

How is the slope typically represented in mathematical terms?

• By the letter Y

• By the letter X

• By the letter M

• By the letter B

What does a negative slope indicate about the mouse population over time?

• The population is fluctuating

• The population is increasing

• The population is decreasing

• The population is constant

For every three months, by how many units does the mouse population decrease?

• 2000 mice

• 4000 mice

• 1000 mice

• 3000 mice

What does the y-intercept represent in the mouse population function?

• The rate of population change

• The initial population

• The maximum population

• The time in months

What is the initial population of mice when no time has passed?

• 7000 mice

• 3000 mice

• 5000 mice

• 1000 mice

How does the y-intercept help in understanding the function?

• It shows the rate of change

• It determines the slope

• It indicates the starting value

• It predicts future values

What happens to the negative two-thirds x term when x equals zero?

• It becomes positive

• It cancels out

• It remains the same

• It doubles

What is the significance of the number 5 in the function?

• It is the rate of decrease

• It is the time in months

• It is the initial population in thousands

• It represents the slope