Fox Population Decline Analysis

The video tutorial explains how to model the declining fox population in a region using an exponential decay equation. Starting with an initial population of 6,700 foxes in 2010, the population decreases by 4% annually. The tutorial details the formulation of the equation, where the decay rate is converted to a decimal, and the base of the exponential function is calculated. The video then demonstrates how to use this model to estimate the fox population in 2018, resulting in an estimated population of 4,833 foxes. The tutorial concludes with a brief summary of the process.

What is the initial fox population in the year 2010?

• 6,700

• 5,000

• 7,500

• 6,000

What type of mathematical model is used to represent the declining fox population?

• Quadratic

• Logarithmic

• Exponential

• Linear

What is the decay rate of the fox population expressed as a decimal?

• 0.004

• 4.0

• 0.04

• 0.4

In the equation p = 6700 * (0.96)^t, what does the base 0.96 represent?

• The initial population

• The percentage of population remaining each year

• The decay rate

• The number of years

What is the formula used to calculate the population at any given year after 2010?

• p = 6700 + 0.96t

• p = 6700 * (0.96)^t

• p = 6700 - 0.96t

• p = 6700 * (1.04)^t

Why is the base of the exponential equation less than 1?

• Because the population is decreasing

• Because the population is constant

• Because the population is unknown

• Because the population is increasing

What is the significance of the number 6700 in the population model?

• It is the initial population

• It is the growth rate

• It is the decay rate

• It is the population in 2018

How many years after 2010 is the population estimated for the year 2018?

• 6

• 10

• 8

• 12

What is the estimated fox population in 2018 according to the model?

• 4,000

• 4,833

• 5,000

• 4,500

What mathematical operation is used to find the population in a future year?

• Addition

• Subtraction

• Multiplication

• Exponentiation