these link is the only video reference.

https://www.youtube.com/watch?v=gVGlA4jdQso

https://www.youtube.com/watch?v=9SOSfRNCQZQ

Scenario: Boa Constrictor Population

The boa constrictor population of an island is threatening the populations of birds, lizards, and mice. Scientists want to know how the population is changing every two years so they can make predictions about the future.

Your Task

You have been asked to describe the population growth and make predictions for the future. Below is the graph of the boa constrictor population you learned about in the video. The x-axis is t, the time in years, and the y-axis is p(t), the snake population for any given year. In this case, t = 0 indicates the year they started keeping track of the constrictor population. Answer the questions below and show work for your calculations.

Analyzing the Data:

1. Is this graph increasing or decreasing? What does this tell you about the population of boa constrictors?(1 point)

1. Looking at this graph, do you think the boa constrictor population could become a problem? (1 point)

1. Identify the following information about the graph. You can review horizontal asymptotes, domain, and range here:https://youtu.be/gVGlA4jdQso. (3 points)

1. Horizontal asymptote: _________________________

1. Domain: ________________________

1. Range: _________________________

1. What is the y-intercept of the graph? What does this mean in terms of the snake population? (1 point)

1. What is the y-value of the graph when x = 1? What does this mean in terms of the snake population? (1 point)

1. The function for an exponential graph isp(t)=abt, wherea is the initial value andb is the rate of growth. What is the function for this graph? (2 points)

1. Use the function from question #6 to estimate the boa constrictor population in 2 years, 3 years, and 4 years. Show your calculations. (6 points: 3 points for showing work, 3 points for the answer for each year)

t: Time in years	p(t): Estimated snake population at time t
2
3
4

1. What pattern do you notice in the table? How is the snake population changing? (2 points)

1. On the day the group of scientists began tracking the snake population, a boy named Larry Cotter accidentally used magic to allow a boa constrictor to escape from the zoo on the island.

1. How would the addition of another boa constrictor to the population change the number of snakes in year 0? (1 point)

1. How would this change affect the growth of the population over time? Explain your answer. (2 points)